That doesn't make sense to me. You haven't "committed a crime" until you've been convicted.
You seem to be saying that you lose the rights merely by being suspected of a crime.
If that is the case, those rights don't actually exist in the first place.
In the US, they have successfully prosecuted people for "fiddling" just like the FBI did here.
The point here is somewhat similar: trying to sue the FBI for unauthorized access to a server would hinge on the relative standing of that law compared to much more serious offences (i.e. conspiracy to murder being the big one) - since the case would have to come from DPR against the FBI, and would thus be subject I suspect to similar tests of standing.
Other people have made the wider point more thoroughly as well - you'd really struggle to prove wrongdoing when all that was acquired was an IP address.
To answer my own question, I guess you could say weev, but I think his troubles really began when he made the pivot from fiddling to mass scraping. I think it's harder to argue the FBI's access was unauthorized when what they were looking at was the "access is denied" page.