OK, last comment: by a combination of fat fingers and the iPhone's auto-complete, I was sending the wrong keyword (hence the reply from Mobivity) and/or the wrong command (fed instead of fwd).

However, I have confirmed that the "fwd voicemail" does not work, whereas other commands do work, even "fwd off." And as I said earlier, the command "fwd voicemail" does work when sent from a different cell phone. Go figure.