To summarize a long response: if there's a statue/trap in the room that goes off when touched, then the GM when improvising details of player actions must not include touching statues.
There's also a little trick to help somewhat with "how does one resolve the occasional conflict of interest between wanting to employ creative narrative without bestowing undue consequences upon those player". Specifically, when narrating something that you're improvising, or in any way paraphrasing what the player said to you, pause a little. This gives the player the opportunity to correct you if you've misunderstood or over-interpreted. So in this case:
"I investigate statue two"
"OK, it's similar in style to the first one. You walk up to within a foot of the statue ... the workmanship is equally good, if anything a little finer. The surface is exceptionally highly polished (or other such improvised little details). It doesn't seem to be breathing like the first one. You look over the whole thing ... and don't see anything otherwise unsual about it. You reach out to touch the mouth like the other one ... roll a save against petrification."
At any of the ..., you pause just for a moment and make sure you're looking at the player whose action you're narrating. A semi-colon's worth of pause is enough for the player to shake their head, or yell "that's not what I meant", or "ummmm... OK, I go ahead", or whatever they want. So if they don't contradict you, they willingly touched the statue, problem solved. Just make sure you pause whether or not there's danger, to avoid making it obvious when the player should bail out.
Ideally, the longer you and your players play, the more of this detail they'll provide themselves, and the above would be a dialogue. But sometimes they just don't have the inspiration to describe in detail an action that you're really excited by, and in certain play styles that's your cue to narrate.
I think you're running into a tension between two gaming styles. But many people do mix those styles in their games anyway, so this isn't uncommon.
In style 1, the GM improvises around player actions as you did, and in particular the GM moves forwards over the boring bits. Maybe the successful roll represents, among other things, the player spending time using their specialist knowledge of traps to determine that statue 1 was safe to touch before touching it. Maybe they didn't do that. Neither the player nor the GM knows or will ever care, because exactly who touches what and when is not material to this scene.
In style 2, there are traps that go off when you take apparently-innocuous actions, and it is the player's job to "own" the risks they take by making every action, and to describe every action in enough detail to satisfy the GM what the consequences will be. It seems to me that this is was common in early dungeons, perhaps as a way of outwitting players who carry 10 foot poles with chickens on the end. So there's a trap that triggers when you take your hat off or whatever, and as long as the GM wrote it down before play started it's entirely "fair" to thereby "punish" PCs for removing their hats, even though that action is typically innocuous. To this day, that sort of exotic trap is present in some games but not others. As you've identified, it's extremely unfair then for the GM to rule that the player has just walked up and touched an object, because deciding what to touch or not is the very essence of player agency in that the game.
Hence my rule. As a rough-and-ready way to combine the two styles, if there's a statue/trap in the room that goes off when touched, then the GM when improvising details of player actions must not include touching statues. Touching things is a significant action in this location, so don't improvise it, just improvise insignificant details for colour. It's easy enough to amend what you said to omit mentions of direct physical contact. Even this will be too much for strong adherents of the second style. But they have it easy because they can just say "no GM improvisation, ever. If they don't explicitly say they touch the statue, they don't touch the statue, they just look at it".
One possible downside of my rule above is that a very alert player who knows you well might notice that you conspiciously didn't describe them touching the first statue, and conclude that somewhere in the room is a trap that triggers on touch. Personally I think this is pretty rare, and when it does occasionally happen, if they're that determined to meta-game then fair enough. They should take their enjoyment of the game where they find it, and they've genuinely outsmarted you.
"This is all very well for general policy", you say, "but how do I recover from my slip in this specific case?". Given that I think it is a slight GM error, I would always aim to recover it in the players' "favour". After all, you knew when you said they touched the first statue, that touching the second statue would be dangerous. So my inclination would be to take your option 1, "how do you investigate the statue?". If the player meta-games at that point, they are (in effect) expressing a preference that GM improvisation shouldn't take their character into harm's way, which is a pretty reasonable preference to have even in a game where the GM improvises freely. If you must, double down on the mistake by adding an unscripted property to the statue: "statue two looks really forboding, it has a sneering expression as if it's silently mocking you. You find yourself pausing for a moment as you go to touch it". They still might touch the statue -- they might think it's some incredibly weak ward and there's treasure in there. But in-game they know something's up with it, so they're entitled to choose to back off without meta-gaming. Nobody's perfect, your players got a free clue, and it's not as if the game would be any worse if that had been scripted. Maybe the sculptor knew the statue was going to be trapped and was unconsciously influenced by that when carving the face. We live and learn.
An alternative would be to rule that unless the player states otherwise, "investigating" a statue necessarily, as an unavoidable part of the action, includes touching it. Unless of course your investigation successfully spots some danger prior to touching it or is otherwise interrupted. This might seem out of line, but if a player says "I open the door" you don't assume that they do so without touching it, so you'd rule that any on-contact trap was triggered. So it's not thoroughly out of line provided you're consistent, although it's not to all tastes. You'd probably combine this with a rule that investigating things by sight alone incurs some penalty on the roll.
Then the GM is not really improvising in the description of touching statue 1 after all, and is not out of line to trigger on-contact effects when the player investigates statue 2. In many games this is too harsh on the players, who might not previously realise that "investigate" implies "touch". But they could (should?) have deduced that fact from your description of statue 1, and if they'd been smart enough to do that and thought it an undue risk they could have chosen not to perform a default, unspecified "investigate" action statue 2 but instead been more cautious. So I think this approach can stand in a "strict player liability" style, even with no advanced notice that to make an investigation check on an object you have to handle it. But it will lead to arguments from time to time and that's why I wouldn't want to get into it myself.
Finally, I would say that I actually don't much like exotic traps that trigger due to precise details that your typical game style doesn't address, precisely because it can lead to ambiguous situations like this. So if your game typically doesn't fuss about who touches what and when, don't put on-contact traps in it. You're just creating a situation that's hard to adjudicate, or the dreaded question at the start of a scene, "before we start this, tell me what colour everyone's hat is please", which warns the players they're about to be punished or rewarded for something completely arbitrary! Use a trigger condition that matches with the kinds of details your players actually give: in this case that could be "the trap triggers if anyone explicitly touches the statue or makes a failed investigation roll on it", although granted that player dialogue was probably a bit of a straw man. But if their standard approach when entering a room is to check it for traps, whatever the language they use to describe that is, your trap descriptions should say whether or not doing it triggers the trap should the test fail (normally yes). Then there's no unfairness because they explictly did the exact thing that triggers the trap.