What I worry about if this were implemented is how weird social encounters might get. An NPC is lying to a PC. What, the DM rolls a Deception check against passive Insight, and that's it? If the player says his character doesn't trust the NPC and thinks he's lying, does that grant retroactive advantage, cause a second, active Insight check (against what, the original roll? passive deception?), or what? Maybe it's metagamey, but does the fact that the DM rolled a D20 when the NPC said something tip the player off that a lie is afoot, whereas "can I make an insight check" requires more active participation from the player?
The results of an active NPC roll vs passive PC skill should be treated no differently than the PC actively making a roll vs a passive NPC skill or an opposed roll (i.e. no reroll unless the circumstances change). I might allow a follow-up active check or force the NPC to make a another check at Disadvantage if the player pursues a line of questioning that compromises the NPC's story.
And of course, any time a PC's passive or active check fails, the player can still choose to believe the NPC is lying.