Neko explained it perfectly. Sharing "publically" means that anyone at any time and come and see the quest solution without doing anything - asking anyone, trying it for themselves, etc. If you share solutions between friends, right on - there's nothing wrong with helping out those who ask or those who really need a hint. Public websites however eliminate the need for any further interaction between people. You browse, you find your answer out of the game, and you're done. Less than ideal for us :}
So far we haven't had anyone actively refuse removing quest information from their public forums or websites - though if we do make a request and get a "No" straight-out, I have no qualms about in-game bans ;P