I'm going to assume then that the 6 Int isn't allowed to solve puzzles, or if the player figures out the King is a doppelganger, he can't say anything until he rolls well on insight check?
I mean, if we're going for parity of stats, intelligence and wisdom should limit what the player can think and deduce. "No solving the riddle unless you roll a DC 13 Intelligence check!"
Okay, but conversely (now arguing the opposite direction of my previous post!), we can easily come up with situations where allowing this 100% always no matter what is just as nonsensical as
never allowing it anytime no matter what.
The most obvious example, of course, is the player who hard-dumps Int, Wis, and Cha, but
portrays an incredibly intelligent, perceptive, charismatic figure--who simply always makes sure to hit the "oh well that's super smart/wise/charming, you can have that without a roll" triggers. That player is min-maxing out the wazoo and paying nothing for it, because they get
functionally all the benefits of sky-high mental stats, with few of the drawbacks.
But there are more subtle ones. For example, while I can be quite gullible at times, if I spend time around a person, most of the time I become pretty good at reading their voice tone, diction, etc. (and visual tells like facial expression and body language, if I see them in person). As a result, I can often predict what a person is going to do, or say, or even
think, well before the consequences land. If I'm playing an Int 8 Paladin,
but I know my GM well and frequently predict what's going to happen next, is it actually realistic, sensible, justified, for that Int 8 Paladin to almost immediately know which path is correct, the solution to a riddle moments after it's been asked, etc.? This is something I intentionally restrain myself from, which is damned difficult sometimes because I
so very much want to blurt out the thing I've figured out, but which my character certainly could not have. (Exactly this sort of issue--that you cannot choose to be significantly more or less intelligent than you actually are--is part of my concern with some claims made upthread.)
Point being,
both things have clearly ungrounded, ridiculous results if applied without restraint. Expecting that stats should
matter, that your character being mechanically foolhardy should
matter for roleplay, isn't a bad thing. Expecting that a good argument, a good idea, even
without mechanical justification, should make a
big difference? That's not a bad thing either. But each becomes grotesque when inflated beyond reason.
And this? This thing right here?
This is where GM adjudication is correctly applied. It isn't possible to write rules that can decide this--because the whole point is the tension between "just follow the rules" and "just ignore the rules" and the problems that each thing can have. That's where you need a human, who can apply common sense. Yes, this does mean that this is an area where GM skill matters, and thus a mediocre GM may fall short, and a bad GM will outright ruin things. But there genuinely is no other option, we cannot do better.
It's a massive error to generalize from this, and the handful of other similar cases where we either must, or should, depend on pure GM adjudication, to the idea that EVERYTHING should be GM adjudication. That, too, is taking a good idea ("There are places where GM adjudication is either necessary, or so overwhelmingly useful that no other alternative is even worth considering") and blowing it way out of proportion into something grotesque and harmful ("EVERYTHING should be GM adjudication ALL THE TIME because who needs the horrible awful nasty RULES???")