Hi,
I am not a novice on mySQL, but I just installed it myself and went through the documentation at http://www.mysql.com
It states there very clearly that the Linux Users and the mySQL Users really have nothing to do with eachother. So you don't need to make an account for every user you want to enable access to the database.
BTW, I tried this too, Linux says:
"Login incorrect"
mySQL says:
"Welcome to the MySQL monitor. Commands end with......."
cheers