You cant delete the Admin Account if its the only one, and a standard user cannot delete an admin account, therefore there must still be one account that is admin on the pc.
There is no way to do that unless you were seriously messing with files under the C:\Windows directory, in which case you can expect weird things to happen. Can be fixed by repairing or reinstalling your OS.
If you're on a corporate network, Group Policy may have renamed it (but not deleted it). If you boot the machine in Safe mode, it may very well "re-appear."
Sounds kinda sketchy to me, I think Windows requires there to be at least one administrator account, I think what he is trying to do is recover one that he has access to, which can be used to access a computer that is not yours.