It would appear that you have not yet learned how to lose. :)
The best, easiest solution available to Harry is to confess.
Even without a wand, de doesn't fear dementors, and dementors fear him. Neither Dumbledore nor Quirrel would be willing to let Harry rot in Azkaban, while they would not break Hermione out.
(I cannot claim credit for this, it was posted on xkcd forums.)
Discussing about the probability of wacky conspiracies is absolutely the wrong way to disprove this. The correct method is a telescope, a quite wide sign with a distance scale drawn on it in very visible colours, and the closest 200m+ body of water you can find.
As long as you are close enough to the ground, the curvature of the earth is very visible, even over surprisingly small distances. I have done this as a child.
The biggest problem with your first alternative is that in it, not having an opinion is equivalent to being wrong.
A lot of the problems with the financial collapse was that various entities and people got to play with the money of other people, with good payouts if they get it right, but no commensurate hit if they got it wrong. While the best outcome is still being right, this kind of situation is bad because it incentivizes taking risk over not taking it. So, a lot of people making those decisions loaded up on as much risk as they could take, ignoring the downsides.