For those interested: https://support.apple.com/en-us/HT201084
In the end, I just let him watch it on my device and he was happy. Myself? I'm of the opinion that whoever design Apple Family Sharing should be ashamed. It's a horribly convoluted system that was either a) never tested by a real family (or they were completely ignored) or b) designed to be horrible on purpose.
We ended up turning it off because sharing apps wasn't worth the "Hey, can you buy this app for me?" coordination.
And then there was all manner of nonsense after we turned it off, too.
I assume there are other weird bugs in family sharing.