I think if Papyrus was dodging the question like Sans did, he would've given more of a bold-faced lie (something where the facts don't line up) or a funny absurd answer (like when he answered the "what if someone was hiding something from you?" question).
Adding to the amnesia-ish line of thought: he is described as "Forgettable" in the murder run! (Perhaps that has a deeper meaning)
And when you talk to him in front of Undyne's house in a run you've killed someone, he says something along the lines of
NOW, I DON'T REMEMBER MURDERING ANYONE...
Don't remember, huh? That's a weird way of phrasing that!
(Granted, that could just be his way of making a cheeky jab at US, but the other possibilities still intrigue me!)
* oh now THIS is where it gets interesting… papyrus appears to be so so sweet, but once you look into it, he’s extremely manipulative and lies even about little things that don’t matter, like if he sleeps or not.
* a HUGE part of this is how he acts in snowdin. if you look at his dialogue with a certain perspective, it becomes clear that he’s just acting. whether it’s for frisk, or as us the player, is completely unclear. hell, it could be both. but he’s pretending all the same.
* a single scene’s examples are:
[ YOU KNOW WHAT’S “SUP”, BROTHER! ] He automatically makes it clear that Sans is his brother without it being necessary.
He acts as if he can’t see Frisk, but from where he’s standing, he should 100% see them with complete ease.
He tells Sans his goals despite him already knowing them.
During the Genocide run, he doesn’t even bother with any dramatics, as there’s no point.
(sidenote, both xbox achievements for snowdin relate to papyrus in a way that calls him god?)
* there’s also him having an obsession with redemption, him saying that he’s a brutal kind of guy, that he’s aware of sans’s pranks that are pulled across time and space, his connection to gaster that he definitely remembers (as he shows sadness at the sight of the CORE despite kind of knowing what frisk is doing), and much much MUCH more.
* there’s a good chance that he just pretends to not remember, either because he regrets it, he wants to move past it, or simply because the past hurts too much to think about