UPMC obviously started out using "University of Pittsburgh Medical Center" and then "UPMC Health System" and used the university seal. They used more of a blue and white motif in their branding such as in the following:
You may still see this is some old signs, but most have them have now been replaced:
Then at some point, probably on the advice of some "brilliant" marketing consultants, they decided to rebrand to just use "UPMC" and use purple as a color because (and this is the reasoning they gave at least publicly) so many other hospitals and systems used blue and white. So purple was supposed to be more unique and soothing, or some such ridiculousness. And they decided to drop the seal and use a mobius strip, one of the stupidest decisions ever, but luckily the mobius was
so stupid that it was never widely implemented and lasted like all of 2 months.
But the purple remained, and they've spend a lot of time and money branding on the simple purple "UPMC" wordmark brand with the "life change medicine" tag line.
Note that the font of the characters used in the "UPMC" workmark has always been the same font used for the university's "University of Pittsburgh" wordmark.
But yes, while UPMC is a separate legal entity from, but intricately intertwined with, the university, it does less co-branding with its affiliated university than perhaps any other academic medical center. Keep in mind many academic medical centers are still fully owned by the university, unlike UPMC. However, 1/3rd of UPMC's board appointments is controlled by the university, while another third is elected by the constituent hospitals that make up the system, and the other third goes to community leaders. The university does actually own the trademarks on both the "University of Pittsburgh Medical Center" and the "UPMC" wordmarks and UPMC still reports as doing business as the "University of Pittsburgh Medical Center."
But I would agree, it is dumb not to find more synergy with the branding between the medical center system and the university. I wish they would reintroduce at least the use of the seal or university crest. And as the athletic department uses the stand alone script P more and more, I would be on board with implementing that, but that would be more of a wholesale rebranding of everything and that would propably be more expensive than they think it would be worth doing for any payoff, at least on the UPMC side of things.