I do not know of any yoga teachers who rent space at a hospital. This does not mean it does not happen, just that I have not heard of it. Karin is correct. In a hospital setting there are liability issues, as well as billing issues. The hospital might make an arrangement with a group to run a program, or a wellness center, like the one she mentions, more than an individual coming in to run a class.
Of course there are also teachers who teach for research projects. I do know people who are involved in this model. Getting into this type of teaching is a little more challenging, and is easier to find if you already have contacts in that community. Though if your skills, experience, alliance status, and so on are really good you could probably make it happen with a bit of research.
Funny thing is I know a number of physicians who are also taking RYT certification to teach yoga. There is a real interest in using it therapeutically.