I don't follow the logic here... no response != assume whatever the hell you feel like.
There's only 2 possibilities here - 1. They didn't see the emails or 2. They saw them, but chose to ignore them. Either way, his choice boils down to killing his idea or launching it and seeing what happens.
It would be utterly moronic of him to kill his idea simply because they didn't respond. Might as well leave that decision to them by launching it and seeing how they respond. If they don't shut him down, then his service isn't breaking their rules. If they do, he's no worse off than not launching in the first place.
He did the right thing.
EDIT: HN is not letting me respond to wmf below, so I'm responding here - Where does he say he knew paypal would freeze the account sooner or later? In fact, the whole point of his emails to them was to specifically ask if his service was compliant with their TOS.
Let's stick to facts and not get into subjective arguments. Your idea of 'ordinary' can be completely different from his or anyone else's idea of 'ordinary'. This is why TOSs, FAQs etc exist in the first place. But since he couldn't find an exact answer anywhere, he emailed them.
There are numerous forms of communication available. Send the email again 3 times asking for escalation to a supervisor. Call them. Send them a letter. Send them a certified letter with return receipt. This is how grown ups conduct business.