Turns Out™ that yes, whilst you can open .fmp12 files in v13 from a server v12 server, not everything gets saved. If for example you upload a file created in v13 to the server, yes, your 13 client will see the formatting, and pop-ups, and styles etc. But you can't save them to the server file, if you change them.
So, plucking an example from thin air, if you spent the best part of an afternoon styling layouts on a server file, and you forgot the server was version 12, then you've lost an afternoon's work.
In which case of course, the law of repeating work already done applies.