What a PC believes shouldn't be determined by a dice roll.
Instead, give them clues depending on the results of their insight check. For instance, if the PCs are interrogating an NPC regarding a string of robberies, an Insight Check DC10 might allow the PCs to notice that the NPCs eyes widened when shown the torn scarf found at the mayor's house, despite him denying seeing it before (or do an opposed bluff vs insight if the NPC has a very good poker face).
This way, you can play with their perceptions a lot. Maybe the NPC they're talking to knows who this scarf belongs to... or maybe he just realized it was a set-up, as it was stolen from him a few days ago, but would rather deny everything in front of the PCs to take care of the matter himself.
Like in real-life, your players will have to decide what they do with the information available to them. If their Insight check is too low, you might give them only part of the information (the NPC seems to be very nervous, which really could mean anything...), which might in turn lead them to make the wrong decision.
This also seems to be suggested by the PHB (p.178) :
Your Wisdom (Insight) check decides whether you can determine the true intentions of a creature, such as when searching out a lie or predicting someone’s next move. Doing so involves gleaning clues from body language, speech habits, and changes in mannerisms.
A good insight check should reveal these clues, but the interpretation should be left to the player.
To specifically address the situation of Insight vs. "Not bluffing", you can interpret the insight check as someone trying really hard to find clues about someone's lies. And when they search too hard, people always end up finding something... So if they roll too low, you could just give them wrong cues about the NPC's behaviour (he seems to be sweating a lot... but that's because he was running to get home before his wife sees her surprise birthday gift, which you don't tell them). As to what could be regarded as "too low", there is a very good guideline in the PHB (p.174) to help you set DCs for such tasks.
Typical difficulty classes
- 5 --- Very easy
- 10 --- Easy
- 15 --- Medium
- 20 --- Hard
- 25 --- Very hard
- 30 --- Nearly impossible
For example, if you think it would normally be very easy to spot someone's lie (Pureferret's example of a paladin whose very nature is against lies), the DC to notice they are speaking truthfully would be 5. On the other hand, if it would normally be hard to spot the lies (the guy from local fence is so used to lying that you can't really tell if he's lying or not anymore, whether you expect him to or not), then the DC should be 20.
As a DM, it is up to you to set up the DCs for such task. Even if the person isn't lying, success could give some behavioral clues to something else ("he looks distracted, as if he's preoccupied with something else") that could be, or not, a plot hook. On the other hand, failure wouldn't reveal any clues whatsoever, and you could rule that a failure by 5 or more (rolling 15 or under against a DC of 20, for example) leads to wrongful interpretation. For example, when dealing with the guy from the local fence, the PCs are expecting him to lie so much that everything seems to indicate it ("he's never looking at you in the eyes, and often checks down the alley behind you" -- of course! he's dealing with illegal goods and is checking for the town watch!).