Found 'a' solution, worked once so far. Create a new squad, make Risen a member of it, and station him, then unstation him. He returns to 'no job' instead of rest, but someone ran to recover him after that.
As he is being carried in, another dwarf is rushing towards him with a bucket, and tracking him as he is being carried - apparently he had 'become forgotten' by the code, but changing his status worked to get him noticed again. Probably worth reporting as a bug (though this is an older version save, so the bug may have already been fixed).
Once in the hospital he went to normal 'rest' status and got diagnosed and treatment started just like normal. Bad news is he appears to have two infections, good news is you didn't do anything wrong (as I bet you guessed) in trying to tend him - your medical set up is perfectly adequate to attempt medical care for anyone hurt if it doesn't bug out on you.
Useful to know about the 'station' work around for this bug. I'd not known about that before I started trying to mess with this, but I'm sure going to use it again if I run into this bug myself!
.... Checked to make sure I could reproduce the fix.
I take back all of the above (save that you're not doing anything wrong, and that this is a bug).
I cannot tell why, but during the 2nd of Hematite (and it's not right as the day changes, but a few seconds into that day), someone will get a recover wounded job. It is NOT always the same dwarf going to recover him. Nor is it always a 'helpful' traited dwarf. And it's clearly not about jobs or the no job tag - though the hurt Risen still has his no job tag.
It doesn't matter if I station Risen or not. Tried 5 times, 3 of them without doing 'anything' but letting time run down, the other two with stationing Risen - made no difference to the timing.
Interestingly, someone's already bringing Risen water when the save starts, 'Ironman' is off to get a bucket. Hope this helps, dunno any fixes, sorry! Hope you report it and offer the save to study.