When you say the OS was reinstalled, did you reformat the drive then install, or did you do an in-place re-install?
If you re-install from the recovery partition without reformatting the drive, it leaves user spaces on the disk intact (/Applications, /Users, and libraries where settings are kept), and only writes over the "generic" OS files. In this case, the Mac mini user account and password would be intact, as would applications and settings.