If the PCs aren't trying to detect signs of a lie, then they don't roll their Insight; you use their Passive Insight as the DC.
In my game, when they do ask to make an Insight check, I do two things a little differently than normal.
I don't roll the NPC's Bluff check. I add 10 and make that the DC.
I only allow one check for the entire group. Everyone can Aid Another but only one person makes the check - and that check stands.
That's pretty much what I was going to suggest as well. The players might
think someone is lying, and call for an active Insight check. That doesn't guarantee it's the case, and in some cases can be a lot of fun, especially if it's role-played well.
I certainly wouldn't roll for the NPC, in fact I would do pretty much exactly as you described - essentially set the DC to detect it as 10+Bluff. Like others, I would definitely be wary of adjusting this number to specifically defeat a character. If a player has training in Insight, and has invested in it, I certainly wouldn't penalize the player for it. In fact, you can take it a step further; if the PC in question realizes a lie, and is trying to be diplomatic, have the player make a Bluff check to try and tip off the other players.
One thing I disagree on though is the use of Aid Another. I'm not sure I would allow a group to collaborate on an Insight check without some sort of consequence, except under certain circumstances. I'm picturing it as, basically, the PCs conferencing as to whether or not the NPC in question is lying. That's not something you can do right in the middle of a conversation - it requires the conversation to at least pause. After the fact, I wouldn't have a problem with it. However, if they broke off a conversation to converse about it, I might apply a penalty to future Diplomacy checks, on the basis that if they don't trust the NPC, the NPC isn't going to trust them either.