XBMC (now dubbed Kodi) is able to mount NFS shares, but it did not work out of the box. Fortunately, the Kodi NFS wiki page tells us what's needed: The options in /etc/exports need to be ro,all_squash,insecure. Unfortunately, the DSM does not allow to set the insecure option on NFS shares.
So I had to log in as root via SSH and edit /etc/exports with vi. The following export works fine:
After changing, you have to activate the changes with
$ exportfs -ar
Editing the shares via the web interface will reset the options :-/