But you "own" your database. Your ISP or parent organization SHOULD give you access to it somehow, even though I agree they should NOT give you access to the database directories.
Another approach once you have access to the database: put in an email address for the user, then go back to MediaWiki and press the "mail be a password" button.
it's not that simple...it's housed in a directory belonging to someone else (long story!). It is being resolved but there are 'issues'...(not unreasonable ones).
In fact i've done what i needed through their admin interface. But i thought this would give me access to the actual php files, so I've clearly got confused about the structure of this thing...i'm only a mortal university lecturer...