DM can make any roll they wants
They also is free to interpret the result any way they wants. However, the described situation is either a misunderstanding, or a not very good DM-ing.
NPC don't make rolls, they take actions
DM then said the NPC was going to try to roll insight ...
If the DM literally says "now this NPC are going to make a roll" it is simply incorrect. First, it's the DM who makes a roll, not an NPC. Secondly, usually players shouldn't know what checks are being made by the DM.
Characters don't make rolls (unless they are playing dice). They take actions, they do something in the game world. It's up to the DM how that actions should be resolved in terms of the mechanics. DM can make any rolls they wants, if they think it is necessary. There are no strict rules like "never make a STR check against an intimidation" in 5e, it is all up to the DM. Remember that DM doesn't play "against" players.
PC don't make rolls, they take actions
Recently I was playing in a campaign and I decided to roll insight on an NPC.
Players shouldn't say things like "I want to roll Insight" (and then roll a die). It's the DM who asks a player "make an Insight check", as a response to players describing the character's actions.
It is normally how the game proceeds:
- DM describes the situation and asks "what do you do"
- Players describe their characters' actions
- DM asks players to make rolls, if necessary
- Players make these rolls
- Basing on the results, DM resolves the situation
If you asks the DM "can I say if she is lying", the DM might ask you to make an Insight check. Or they can use a passive check. Or ask you "how do you do that". But you are always supposed to describe your character's actions, not your rolls.
More information about Insight specifically: How to use, and not to overuse, Insight skill checks?