Depends what sort of fighter you want to be. Your instructor could be being very close minded. I believe one of the Diaz brothers said that people getting injured all the time in the gym lifting weights is stupid, they should be rolling, sparring and practising technique instead. Neither of the Diaz brothers have much power at all, but they're really good. There are loads of fighters who clearly aren't big weight lifters.
Obviously if you want to be a wrestler, then strength is a big part of it.
The way I see it, if you have good indurance(not just cardio, muscle indurance is very important too) then you're good to go. If you have good indurance and enough basic strength to squat your own weight + your weight again a few times in 15 minutes, then that'd all you're going to need.
I suggest some sort of circuit training to supliment your mma trianing. That will really work your muscle indurance and cardio.
NYBA Champ @ 170!