Nonetheless he is right. As far as I remember Vim is based on the code of an editor that was similar to vi, and not vi itself.
Vim can be invoked to conform to the vi standard, although usually it only gets used that way when a vim user is on an unfamiliar machine.
[0] http://pubs.opengroup.org/onlinepubs/7908799/xcu/vi.html [1] https://en.wikipedia.org/wiki/Single_UNIX_Specification