Definitely the easiest way to fix that problem if you have an otherwise empty database is just re-install it. But there is a script installed with MySQL that creates the empty permissions tables so you can recover. I can't find it mentioned in the online docs, that's all.
As for the problem with phpMyAdmin; that's the configuration of phpMyAdmin. It can do security a few different ways. It sounds like you want it to use the MySQL users, which by default I don't think it does. The configuration file has the information to change it.
Wade.