And how does the DM make that decision? To me, it seems that is exactly what the Deception skill is intended for.
That seems to be a narrative decission to me. Some npc's are good liars and you can't tell that they are lying, some are bad liars and you might be able to tell, and some are terrible liars and no check is needed. There are auto-fails, auto-successes, and a few edge cases. For the most part, I lean towards auto-fail. I assume that all my npc's are competent and try their best to lie. If the players want to find out if they are lying, they have to catch the npc's on falsehoods or inconsistencies in their story, rather than a lucky dice roll. To me that is far more exciting roleplaying wise.
While autofailure is, in the abstract, always one possibility, personally I don't think it makes a very good default independent of circumstances. Can you give any additional insight (haha) as to why you do this?
Nice one.

I do this because I want my players to actually pay attention to what an npc is saying. I want them to remember what they know about the story and use that to determine lies and falsehoods. When a person lies, just like in real life, you usually can't tell. But what a player can do, is pay attention to what an npc says, and to subtle cues that are given while he says it.
When a player searches a room, I ask them
what they are looking for. If they want to disable a trap, I ask them
how they want to disable it. I do the same with social checks. You can't just tell a person is lying, but perhaps you can tell if he's nervous? Or whether the things he says are factual? The player needs to state an approach, and then I determine if it's an auto-fail, auto-success or a dice roll.
Ok, I assume this is somewhat lighthearted and you really mean that you think he would be caught (regardless of what you might want), otherwise it certainly sounds a bit railroad-ish.
Some npc's are just terrible liars, or the thing they are trying to lie about is so painfully obvious, that the players would be fools to believe it.
Is your procedure in this case to rule an autosuccess or is this the case that you mentioned above in which the NPC would exhibit a 'remarkable behavior'?
I would have the npc show a remarkable behavior, or act him out in a way that makes it painfully obvious that he's lying. I'd have the npc misspeak for example, and almost blurt out something he didn't mean to say. Or perhaps the npc simply cracks under enough pressure by the players, and confesses to lying. Either way it's an auto-success.
I don't understand the distinction between being able to tell if the one NPC is "telling the truth" and being able to tell whether other NPCs are "on his side". To me, these both seem to be instances of being able to discern something about an NPC's mental state. What is it that causes you to treat them differently?
In my opinion, you can't read lies, but you can read emotions, gestures, looks. How those clues are interpreted is up to the players. I always expect my players to state an approach to what they are trying to achieve, and then I decide if the outcome is in doubt.
So when an npc says he has the players surrounded, I don't want my players to say "Can I make an insight check to tell if he's lying?". Instead I want them to say something like "Does it look like he has a lot of allies in the bar?" or "Do I see other people with weapons?" or "Does the npc seem nervous?" or "How does the rest of the tavern respond to these threats?"
Depending on the stated approach, the players may have to make an insight check, but it might as well be a perception check, or no check at all.