iserith
Magic Wordsmith
Nobody here is imposing, advocating, or even tentatively suggesting any restrictions on your character's ability to attempt Strength-based tasks. What a character wants and tries to do is part of their motivation, not their ability scores. A low-Int character could similarly go around trying to prove his or her intelligence, like Otto from A Fish Called Wanda. But Otto is still stupid. He's acting to the best of his very limited abilities, but they're still very limited abilities. He draws stupid conclusions from what he reads. He comes up with stupid plans. He does stupid things. What we're concerned about here is players using their intelligence and knowledge to draw conclusions, make plans, and do things on their character's behalf that are completely out of character. Otto thinks the London Underground is a political movement. Kevin Kline (or scriptwriter John Cleese, if you prefer) presumably knows it's not. Which information should Otto act on?
If Otto's player established his or her character as believing that the London Underground is a political movement, then Otto's player would be contradicting that which was already established by acting as if Otto's did not believe that.
Before it is established, however, Otto's player is free to decide what Otto thinks the London Underground is. He or she may say Otto believes it to be a political movement or a railway system as he or she likes. If Otto's player said something like, "Otto tries to recall what the London Underground is based on what he's read ," then the DM can decide to call for an Intelligence check with an appropriate DC. At this point, Otto's Intelligence score comes into play by imparting a -3 modifier to the check (if Otto has an Intelligence of 5) and he is 15% less likely to recall what it is than another character with a 10 or 11 Intelligence.