Does this mean that I can connect to an NFS server saying my UID=0 and get local root?

Usually, no. NFS defaults to "root_squash," which silently changes UID=0 to the UID of the `nfsnobody` user.

However, in the /etc/exports file, you can (but shouldn't) add the share option "no_root_squash" which disables that.

So, root access is slightly protected. But all other users are wide open.