There is one other possibility... your disc drive may be broken or dirty. So, before you tell the hospital they gave you a blank disc you will need to see if someone else can open it.
He already did that, and it worked:
"... the info is there (a friend with a PC had no problem), ..."
I agree that the disc drive itself may be broken or dirty.
To test this, insert a known-good disc, such as an audio CD, or a movie DVD. The Mac should recognize it. If it offers to eject or format, then try another known-good disc. If both fail, then the problem is almost certainly the drive. One option at that point is an external CD/DVD drive, connected via USD. They aren't that expensive, and may well cost less than repairing or replacing the builtin drive.
Or as TheEasterBunny mentioned, it may be that the disc wasn't burned correctly (session closed). That's harder to test for, and if the disc drive is broken or dirty, isn't testable at all. So determine the quality of the disc drive first, then when the drive is known-good, test the disc as necessary.
Personally, I suspect the disc drive. A Mac mini with Lion is probably at least a couple of years old, and if the CD/DVD drive hasn't been used much during that time, it may have failed with no indication. If the mini runs for long periods of time, the fan pulls in air through the drive slot, so dust can easily accumulate.
FWIW, I've gotten Xrays on CD-R in both JPEG and TIFF formats (.JPG and .TIF suffixes). The TIFF ones came with a Windows app on the disc. I had no difficulty reading the disc in my Core Solo Mac mini at the time. Didn't need any special software; Preview.app worked fine.