Tutors seem to check local stat files instead of server stat files when displaying whether a Pokémon can/can't learn a move. It won't actually let you teach something the server doesn't have in the stats file, but it also won't let you select a move a Pokémon can't learn locally but can on the server (for example the missing moves from the move to Gen 8 that aren't in the stats files properly [see my previous ticket #15812]).

To replicate:
Add a move to the server's stat files for a Pokémon under tutor moves (or transfer moves) that can't be learned by default. Try and learn that move on the server with your default files locally. It will say you can't and won't let you select it. Then add the move to your local files, now it will let you.

Also try adding a move to your local files that isn't in the server ones. It will now say you can learn it (but if you try it shouldn't actually teach it).

Hi, and apologies for the late response.
This issue is still present in the latest 8.3.6 release, see this report for more details. I have added a comment to that ticket suggesting that tutors checking local stat files is likely the source of the issue. Thanks for your report!