Bawylie
A very OK person
Back to the OP. I can see it now. The group has been hired by an insurance company to investigate a jewelry store heist. They're questioning the shopkeeper.
DM/shopkeeper "So I locked up the store as usual, set the normal traps and went upstairs to bed."
Player: "You sleep above the shop?"
DM/shopkeeper: "Yes, it's part of the compensation, and I'm single so it works well for me."
Player: "So no witness and you didn't hear anything at all during the night."
DM/shopkeeper: "No witnesses and no I didn't hear anything. But this building is very solidly built for a reason."
Player: "And there was no sign of forced entry, the traps were still set."
DM/shopkeeper: "That's right. In fact the traps are supposed to ward against magical entry as well."
Player: "I don't believe him, I think he's hiding something."
DM: "Okay."
Player: "Umm...can I get a read on him? An insight check?"
DM: "No."
Player: "What do you mean?"
DM: "The players don't get to ask to do skill checks. They declare action and intent."
Player: "So...I'm studying him closely looking for signs that he's being deceptive."
DM: "Okay"
Player: "So can I roll an insight check?"
DM: "No"
Player: "Why not? The PHB says I can use an insight check to try to determine their true intentions."
DM: "Because I didn't ask for an insight check."
Player: "What the f... okay. Mother may I have an insight check?"
DM: "No."
Player: "Dude, I have investigator as my background. I took Inquisitive Rogue so that I'd be particularly good at it. I have the Ear For Deceit feature and expertise in insight. This is kind of a big deal for me. Can I roll an insight check?"
DM: "No, asking for a check does not entitle you to a roll."
Is that seriously how this could go if the shopkeeper is telling the truth? Or lying for that matter, and you just don't think there's a reason to suspect the shopkeeper? Because honestly, I wouldn't want to play with a DM that did this.
Because in my game it would be
...skipping a few lines...
Player: "I don't believe him, I think he's hiding something."
DM: "Give me an insight check."
Player: "20"
or even
Player: "I don't believe him, I make an insight check of 20"
My response as DM is going to be something like: "He seems to be telling the truth."
And so on and so forth. Or maybe I'd reveal that the shopkeeper seemed nervous because to me the shopkeeper knows how bad this looks. Or maybe he's as cool as a cucumber and just really good at lying.
Someone else adequately answered this but this one is funny because I’ve actually done this interview myself for a similar situation and I’ve run this type of thing in a game.
To answer: my players aren’t asking to make rolls, so that bit doesn’t come up. Instead they might tell me they suspect, and look for signs of, deception.
I might ask for a wisdom check, and a player might respond “hey I’m trained in insight.”
In this circumstance I’d have an untrained character roll a wisdom check, but a character trained in insight might glean: “The shopkeeper is nervous and frightened, as anyone in this position would be. They’re afraid they will be blamed for the theft and they’re nervous because they can’t tell if anyone here is on their side. There is no indication that they’re being misleading or hiding anything.”
This also answers the OP (if anyone can remember the OP from the before-times). The DC to determine someone is telling the truth depends how you try to verify that - and for a person trained in insight, an automatic success might be most appropriate.
Side note: this approach can also cover the “the DM didn’t make me roll so I know X” issue. Being trained in insight alone is enough to cover a LOT, so a roll itself isn’t demonstrative of anything except an uncertain outcome. A variant can be found in the DMG where if the score is high enough, you can have auto-success (or something like that). I just skip the math and assume a trained character is sufficiently competent to get an auto success absent some notable cost, consequence, or interference.