Yes, the TRANS PROG FAILSAFE can be initiated by a number of non-tranny sources (sensor, alternator, etc.) and may not reflect a tranny problem, per se. I suggest that you have the ODB cleared. This will restore you to normal mode. If the default mode recurs, that will indicate your problem is real and still there.
Anecdotal info: My e39 spit the same code on a wet cold day. The dealer spent 2 days attempting a diagnosis and they wanted to replace the tranny (at only 48K). I had them clear the code and reset the OBC. 2.5 years and 25K miles later, the problem never came back. The only good thing is they only charged me one hour labor $115 for reading and clearing the error code.