If I had a character who wanted to use the "actually knows but voices tell her not to say" explanation, I would insist that they obey the dice. So if they failed a lethal intelligence check (to identify cyanide or whatever), I would expect their character does what the voices say even unto death. Thats the whole shtick of the character.
I agree: to be fair to the game mechanics, the player is going to have to play the character this way. And the DM is going to have to withhold information from the player that the character "knows". I think this is precisely the problem with playing a low Intelligence like this. It creates an artificial player/character disconnect, and it paints the player's roleplaying options into a corner, effectively taking control of the character out of their hands.
Consider how this character might play out in a book or movie, without being tied to a low Intelligence score mechanic. She identifies the cyanide, and then has to decide whether her commitment to her patron is worth risking death for.
This could be a key dramatic moment. She might dramatically renounce her patron and pour out the drink, or she might dramatically down the poisoned wine. Either way, it's good fiction. But playing this character at the table as Int 5, you can't get
either dramatic benefit. The character can't choose to pour out the drink, because then she would be benefiting from an Int score she doesn't have, and when she does drink, it's not a dramatic moment, because the DM hasn't even told her the wine is poisoned. It's just, after the fact, "You take 38 poison damage, because the wine was poisoned. You knew it, but you chose to drink anyway because of your patron."
But if you build this character as somebody with high Int who just lies a lot, then the player can know what the character knows and can make the same decisions the character is making.
There's an argument in the other thread that if the player solves the riddle, he need never roll. He only needs to roll if his declaration introduces doubt. If the player just has his character state the answer, no roll needed. This works with this construct because it substitutes the player's ability for the character's ability in all cases that the player can work out action declarations to avoid the need to roll.
Personally, I find that to be as bad as direct cheating. Gaming the system so you don't have to cheat to get the ends you would otherwise need to cheat to achieve is a distinction without a difference.
If a riddle is a special, once-or-twice-a-campaign event, then I have no problem with the players solving it irrespective of their characters' Intelligence scores. It's an old, old trope for the fool to come up with the answer when everyone else is stumped. It wasn't Gandalf who got the Fellowship through the Gate of Moria, after all. So if the game plays out that way, great!
But if riddles are a regular thing and the player of the low-Int character is regularly solving them, I'm probably going to start asking for some Intelligence checks. Like you said, consistency is key.