PhDs are a little different because they really vary based on your field and on your advisor. (at least in the US and in the sciences.) It's your advisor's job to make sure you learn all that you need to learn to do research. Schooling is just a distraction that you get done with on the side and as quickly as possible so you can get back to research.

In the best cases, your advisor will also introduce you to the research community if you want to be a researcher, or help you get teaching gigs / TAships if you want to be a teaching professor, or help you get internships if you want to do industry. The university is just the context in which you and your advisor work, and the degree tells your peers that you've gained a certain level of expertise.

Consequently, my primary gratitude is to my advisor, not to the university.