I’m having kind of the same problem, I wrote about it in this thread: thread.
For me it looks like osmc isn’t setting up the correct group and guest permissions for the external drive.
When I try to chmod the drive, it fails with a weird error message I forgot.
I’m currently formatting my drive from exFat to ext4 to see if that is the reason the permissions aren’t set correctly. (You read a lot of self-contradictory stuff if you google long enough…). Time will show if the permission errors still appear - I’ll report back then.