He wasn't prosecuted for logging in and looking around. He overtly did copyleft type things like finding ways to take copyrighted journal articles and release them into the public domain. Overzealous prosecution for sure regardless.
> On July 11, 2011, he was indicted by a federal grand jury on charges of wire fraud, computer fraud, unlawfully obtaining information from a protected computer, and recklessly damaging a protected computer.
> On November 17, 2011, Swartz was indicted by a Middlesex County Superior Court grand jury on state charges of breaking and entering with intent, grand larceny, and unauthorized access to a computer network.
> On September 12, 2012, federal prosecutors filed a superseding indictment adding nine more felony counts, increasing Swartz's maximum criminal exposure to 50 years of imprisonment and $1 million in fines.
The only civil copyright proceedings were JSTOR settling with him out of court.