The statement in the OP is credible. Lets take a scenario where you have two candidates (whose personalities are both likeable), one from Yale university (one of the best in America) and the other from Oklahoma Community College - it wouldn't be a hard decision for most people to make. It is the same with UNSW or USYD versus University of Western Sydney, Charles Sturt University, Notre Dame University, Southern Cross University etc...
UNSW/USYD are regarded as more competitive and better institutions by industry.
Although if you want to do medicine or whatever it is better to do it (at UWS if you have to) than to not do it at all.