Ken,
I bet if we had some real numbers, the statistics/odds would be in your favor that you can tow with it on without incident. You know how it is, if there were even just a few crashes involving RVs with open gas valves that turned into infernos, the media would be all over it like ugly on an ape. Since I don't recall hearing about it much, it seems that the tragedy potential isn't realized very often (and that's great news!).
I think a lot of people do tow with it on - based on our responses on TDR. So the percentages seem to be in the favor of those who do. Even if you do tow with it on, the conditions have to be right for the potential to be reached.
#1. You have to have an accident.
#2. An LP bottle has to be involved.
#3. The bottle or line has to be breached and a leak has to occur.
#4. There has to be an ignition source.
To get to #3, things have to be bad. #4 could follow pretty easily, though. So, the odds are probably in your favor that you'll be ok.
So, am I disproving my case? Nope, I still will try for that little bit of extra safety - and peace of mind. But I don't want to sound like a Chicken Little, either. If asked, I recommend towing with the valves off. But I'm just expressing what's comfortable for me. Of course I hope that we all have safe travels all the time, no matter what our practice is on this issue.
OK, group hug time.
Dave