Yes, inheriting a server always an 'adventure' - especially with no former server admin notes/etc. And yes, nginx isn't apache ... for sure.
You might have found the issue.
About ownerships/permissions ... check the o/p of moodledata/filedir directory recusively. You are able to upload files already to the moodle so the o/p on repository directories should be same as /moodledata/filedir/00 as an example.
Not that you'd be leaving your position any time soon, but for a reminder to you and maybe the next admin, here's a suggestion:
Create a hidden System Admins category and course. Assign no one roles in either. Use Moodle to document your moodle. A page on nginx config is in order.
'spirit of sharing', Ken