The origin of the word idiot is “one’s own,” the same root as idiom. So originally an idiot was someone in his own world, someone who takes no outside input. The historical meaning carries over to some degree: When you see a smart person do something idiotic, it’s usually because he’s acting alone.
The opposite of an idiot would not be someone who is wise, but someone who takes too much outside input, someone who passively lets others make all his decisions or who puts every decision to a vote.
An idiot lives only in his own world; the opposite of an idiot has no world of his own. Both are foolish, but I think the Internet encourages more of the latter kind of foolishness. It’s not turning people into idiots, it’s turning them into the opposite.