If files end up in a different directory because the user rearranged the filesystem under your nose, that's on the user. Most applications would deal with that by telling the user not to do that.

If your sensitive logs end up in the webserver root because one thread used chdir to temporarily change the working directory it's on the application writer.

Or to put it another way, the filesystem as a whole being shared mutable state does not make the current working directory being shared mutable state between threads any less of an issue.