My objection is that there has to be some basic consistency to what mental stats mean, just as there is basic consistency as to what physical stats mean, or you have an unhelpful and rather unfair double-standard.
A similar conversation was recently had in the thread about using out of character knowledge. I believe that the view in opposition to yours (and to my preference) is that if the player wants to have their character think something - regardless of the mental stats - then they can. If they want their 3 INT character to think they know how to make gun powder, or all of the simple machines, or a printing press, or what the MM says about all of the monsters, or how integral and differential calculus, then that's fine. They might be wrong in that particular game world. While there were clear prohibitions of this in 1e and 2e, they do not exist in 5e. As such, it might be argued that requiring play that way is a house rule (and not just "common sense" as I might still say in spite of having found no 5e rules requiring it).