Tenet and Columbia are both for-profit chains that have bad reps. I think both earned their bad pr, but there are exceptions. I worked at a Columbia hospital that was really good. I have no idea what the Tenet hospital in Philly is like, but I do know that you don't have to work for them to get that money. It's a federal program:
I think the way it works is the gov't has a list of "critically understaffed" hospitals (most are on it, I think- LOL) and as long as you work at one for 2-3 years, you get the repayment money. I think the amount varies depending on how long you commit to work at a short-staffed hospital and I am pretty sure you can change jobs and stay eligible, as long as both hospitals are on the list.
If Tenet has an additional $20K on top of the federal money, it might be worth it, but I would be surprised. My hospital advertises big buck tuition payback too- and none of the money comes out of THEIR own pocket.
Find out if they are talking about the federal program- if they are, you have lots of options. The fund website has a list of eligible hospitals on their somewhere.