Good going for working it out.
If that hadn't worked, I would have suggested looking in /etc/ftpusers to see if it was listed there. Counterintuitively, anyone listed in /etc/ftpusers will
not be able to use FTP or SSH, etc. I'm not quite sure why the file's called that myself, but, yeah.
By the way, the other thing to watch out for is that if you specify a login shell that's not listed in /etc/shells, most FTP servers will do the same as you described and not let the user log in - so just putting /bin/false as a login shell won't help unless it's also listed in /etc/shells.