Everything else I can chalk up to personal preference, but this here is a difference in an approach to fiction that, while I will admit the PHB spells out, is counterfactual to, well, actual reality. Which is to say; memory does that work like that. That's not to say that nobody actively attempts to recall lore or information about things, it's just that that is the exception rather than the rule, and one that is almost always prompted by a direct question (such as a school exam or trivia game). But memory, and knowledge, are generally much more passive. And while I am loathe to use passive checks in most instances, because this is a ultimately a dice game and I like it when I/my players get to roll dice to determine uncertain outcomes, I can recognize the role passive perception at least plays in not tipping one's hand too early as a DM. I do not like, however, "passive knowledge", at least not in D&D, because it treats one set of proficiencies differently than others, and I think a "you must have have this high a bonus to know this thing" DC sets knowledge skills apart from other more active skills that seems less than ideal to me. On the other hand, it strains my sense of and approach to the fiction of the world to treat character knowledge as a repository that only be accessed if players decide to boot it up.
I just think it's bad form (and bad for the game) to withhold from players knowledge their characters might (or do) know just because they don't think to use the "recall lore" action in the moment.