It's medi (as in middle) terranean as in 'of the earth'. If you've found people who spell it with two ts you are simply demonstrating the internet's limitation as a source of authoritative info. Lose and loose have a strange interchangeability on the net too.
Medi.... is going on a business card (as Seraph is almost ready for charter over here /forums/images/graemlins/smile.gif) so the spelling has to be correct.
I know the SA's aren't too bothered about spelling or pronunciation eg "My car won't fit in my grudge (garage)