I'm typically a GM, and to speak honestly and frankly, I never care if players "mix" knowledge.
It's never worth it to police (because doing so requires you to call players out for 'meta-gaming' and then I feel like a jerk for accusing a player of something, they feel like a jerk for stepping over a line in the sand, and everyone at the table feels awkward because now they have started thinking about what the player just said and are worried about that clouding their previous thoughts.. you can't go back, but the accusation forces everyone to try and pretend the thought never happened).
It requires players to complete excessive mental gymnastics (which you two, suddenly finding yourselves as players, are discovering first hand how awkward those gymnastics are). I'd rather focus mental processing on imagining the scene than on trying to keep separate two bodies of knowledge. Also, it makes players afraid to get into character for fear of getting it 'wrong'. If this is being enforced then getting it 'wrong' entails social awkwardness, which many players want to avoid. This is extra strange when you think about it, because it's the player who made the character so why does the GM get to decide what that character does and doesn't know? Which leads to the last point...
No character is so fully detailed that all aspects of their life and all things that they could be said to know can be specified. Which is to say, you can't specify all of the knowledge your character has and so how can you be expected to keep it separate from another source of knowledge. These characters didn't just appear here in this little town as blank slates, they have histories, exploits and backgrounds which are at best vaguely filled in.
... Sorry for the rant, it's apparently a soft spot for me.