Hi,
Congrats on making your choice for USC. You'll have a great time down there, a couple of my friends were down there for undergrad and really had a great time.
Although what you say is true about commitment and passion towards public health studies, in respect to a PhD adcomm member, and knowing a couple personally myself (I work with two), where you come from definetly matters. Its the sad truth but this is what's already known throughout academia as there is a hierarchy of who goes where and to which PhD program. Granted, there will be many PhD programs that will take students, but those who are gunning for the top programs in the country (Harvard, JHU, UNC, UW, UMich, etc..) find that they will be in competition with the best and the brightest from all walks of life and all different schools...the truth of the matter is, acceptance into a good PhD program is as difficult as getting into a good medical school.
If an adcom has the choice between 2 students lets say one from "Prestigeous School A" and "Good School B"...the winner will mostly likely (and in the far majority) be the student who went to Prestigeous School A. This is just how academia works as most of those adcoms, if you look at their CV, have degrees from the prestigeous schools. I've done my share of looking and have found that I seem to ALWAYS be running into MPH/PhDs from the top 5 public health schools holding the majority of positions at Public Health schools.
The reality of the matter is, when applying to a PhD program, most students come into the application cycle at near even par with their competitors as most students have the same mindset of "getting out there, doing lots of community service, etc" but the only thing that will differentiate those students ultimatly comes down to empirical stats and where they went to school.
I'm not saying that USC is not a very good school. USC is very unique in it's service reach and the location. Some of the top hospitals in the country are in the region and some of the largest health disparities find their home on Southern California. You'll get to see things that other won't get to see on a day-to-day basis and you'll have a head start in many different aspects of PH studies while there.
Congrats and good luck!