Many research studies in the U.S. are required to do "structural" scans (high-resolution T1 or T2) and send them to a safety read by a radiologist, for liability reasons. At very least, this scan should be available directly from the hospital imaging department. If you are lucky all the data will have been sent through the hospital PACS and the imaging department will indiscriminately dump everything. At a research-only center it might be more complicated because such images are likely sent off-site for the safety read.
What got me interested in getting the data was this: [1]. It might be difficult to work with, but there was a lot of motivation to learn it.
[1] http://nbviewer.jupyter.org/github/GaelVaroquaux/nilearn_cou...
And if you're interested in having the data for your own purposes, there may still be some liability concerns for the researchers. There's always an agreement to keep MRI data under strict supervision to avoid leaks of personal health information, so providing those data to participants (safeguards or no) could potentially count as a breach of protocol.
Though, when I found that out, I did some naive scans to see if they had any public webservers that would have the research information. I didn't see any, but there were a huge number of HIPAA violations where many, many computers with health information were exposed directly to the internet. Their security team told me that it wasn't anything to be concerned about. A HIPAA complaint didn't go anywhere, either. Already spoke with a journalist to try to get some traction on it..