Earlier quoted context omitted.
> service outages at the time the imaging was conducted That whole "correlation is not causation" maxim comes to mind here.
It's part of a greater collection of evidence. Evidence doesn't have to be mathematical proof. A common theme (from what I can tell in law) is that something can never be proven to the rigor of a mathematician, so what happens is you build up piles of "coincidences" until a reasonable person would be hard-pressed to believe they are only coincidence.
http://en.wikipedia.org/wiki/Reasonable_doubt
None of the items taken by themselves are enough to convict (e.g., other people would be tweeting about Silkroad 2 at the same time), but you add it all together (server in his name, piles of unexplained cash and large purchases, tweeting about it, accessing the servers from his machine, etc., etc.) and it starts to look really bad.
Plus he's also confessed, apparently.