You have two basic choices for how to have your players roll their dice:
- Ask them to make their rolls in secret, and trust the results they tell you.
- Ask them to roll their dice in the open, so that there's no question they're telling the truth.
If you take the first option you must trust your players and accept what they tell you!
You need to be able to trust them and work with them, and they need to be able to trust you and work with you. The game experience is going to be quite poisonous otherwise - I'll talk about that later. You've chosen a method which requires trust, so provide that trust.
If they are fudging, accept it for the fun value. You can't tell if they're doing it anyway. This is exactly the same as DMs who roll behind the screen: the players may suspect that sometimes the DM went easy on the nearly-dead target and fudged a miss, but the players should be able to trust the DM to make the game fun for them. That doesn't mean you need to pretend it isn't happening - just accept it and be okay with it, and continue playing.
Higher than average results are entirely possible.
They're improbable, yes, but not impossible, and doesn't suggest cheating.
Today, I played my first Pokemon TCG game with a friend. We were doing a lot of things that called for coin flips. Out of at least a couple of dozen coin flips, only four were tails. It's highly improbable, but it happened.
Some players somehow roll quite well on average. We have a member here who is sort of the example of the opposite: he consistently rolls improbably low on average, with any set of dice, and even with a dice tower. It's incredible, but it happens, and has been happening this way for years. Here's the records from one session which was played in person and not online - no fudging occurred.
Some don't have precision cut dice, so the unevenly rounded edges and corners make certain rolls slightly less probable - this is not weighted dice or conscious cheating, it's just a flaw in the manufacturing process.
Bottom line: If you want to use a dice rolling method requiring trust, extend that trust, or don't use that dice rolling method.
What if you can't provide that trust and accept their rolls?
If you keep going like this and can't trust your players, you'll end up relating to them as cheaters and you'll probably be irritated by their cheating - whether or not they really are. That's going to be really fun for them being treated like cheaters, and I say that with massive amounts of sarcasm. They won't be able to trust you to be impartial with them because you won't trust them. The experience will be very toxic and toxic experiences destroy groups and any fun value in games.
So, if you cannot trust them, tell them you want to switch dice rolling method.
Be straightforward and honest in telling them why: the results they're getting bugs you, and you have no way of knowing they're cheating or not, and you'd prefer to trust them but you'd rather just find a rolling method that eliminates any reason to be suspicious to begin with - that way, you can all have fun without you needing to be concerned.
Find a dice roller that lets you view each others' rolls and use it.
If you do this and the average results change, don't use that as a reason to suspect they were cheating. The success rates they were having were entirely possible, however improbable, and they may not have been cheating at all.