As long as it's a quality PSU. Generic and/or weak PSU's at 500w aren't the same thing as a quality 500w PSU. Don't assume that all 500w PSU's are made the same.
Well, recommended PSU for GTS 450 is 400W, and for HD 6770 its 450W. Of course though, if he has a crap PSU which cannot deliver enough power - it will not run - you are right, it needs to be a quality PSU.