This is a category error when it comes to copyleft licenses like the GPL. It has nothing to say about usage.
"If, on the other hand, the licensor and licensee both have some obligations (in OSS, this is usually when you modify or redistribute the source or compiled product), then it's basically a contract, no matter what RMS claims."
No it's not. There are no pre-agreed terms, penalties for violation, expected compensation for services provided or anything like that. GPLed software is copyrighted. Copyright law says you have no rights to copy it or make derivative works of it whatsoever. The license permits you to do so.
"Why would you trust what he says about contract law, a field where he has no professional training whatsoever?"
Because, surprise surprise, he has advice from people who ARE trained in the law.