Yes, it's saying it's a directory and terminal is sitting looking at me. WIth contempt.
Try this, with lowercase R.
sudo rm -r /Volumes/Owen\ photography\ drive\ 1/.Trashes/501/Backups.backupdb
I seem to have to put my password in an AWFUL lot! It wasn't like this on a different mac.
That is normal.
You are still the admin, but you have to authenticate.