In US criminal cases, defendants are presumed innocent, and prosecutors must prove guilt "beyond a reasonable doubt". So defendants don't need to prove anything. They just need to invalidate prosecutors' evidence. But defendants are often toast if they lose the expert witness credibility contest.
On the other hand, the prosecution might overlook history because it's in Firefox instead of IE[1]. It's kind of tangential to this subthread, but to tie it back somewhat, that article notes that some browser history entries came up in court, and this bungling doesn't reflect well on the competence and credibility of computer expert witnesses.
