It appears this might be related to dropbox (mis)using statfs's f_fsid field as part of its authentication system. The dropbox devs apparently assumed that this field was stable, but on XFS (for instance) it can change.
I'm not surprised, though. Fancy copy-on-write filesystems like btrfs have some other subtle gotchas. If you allocate (like, really, not as a hole) a big file on btrfs and mmap it for write, you might see a SIGBUS upon writing because btrfs needed to recompress a block and the new compressed block didn't fit where the old one did.
I've gained a new appreciation for the predictability and simplicity of ext4.
Once saw a system that used inode numbers as "unique identifiers for files on local disk" and it turns out that on Linux / ext filesystems, they're not unique (they get reused if you delete a file and then create a new one). That team just decided to not support Linux at all.
dropboxforum thread here: https://www.dropboxforum.com/t5/Installation-and-desktop-app...