There are kinds of evidence that I would find convincing. Testimony from police that he had certain things open on the screen at the moment of arrest (as in the Silk Road case). Or hidden-camera video of him at a terminal, doing something bad. Or an audio recording of a voice call in which he tries to do social engineering.
I haven't found anything like that. If someone posts a link, I'll certainly change my mind. But for know, all the evidence I know of is of a sort that one person could've forged.
That is kind of a serious problem. It's like the "open WiFi" defense. It's completely plausible that someone else actually used your WiFi or compromised your computer, but at the same time some people have this visceral reaction to allowing it as a defense because it's so hard to disprove and can be used by anyone.
Often when cases like this are reported, the evidentiary details don't make it into the story. It's easy to understand why someone would have a problem with a conviction when all the information they have is the BBC's 10,000ft summary.
What's worse is, that 10,000ft summary can bias you by framing the whole story in your mind. You're skeptical right off the bat. That's probably always healthy! But it's good to know how your mind is being primed to digest new information, too.
Obviously, sometimes you get the details and the case doesn't get less murky. The Aurenheimer case is an example; I don't have a clue what to think about it, and would like to think that whatever my prejudices are, I'd have been a not-guilty vote in a jury based on that doubt.