I had this problem a couple times over the winter in our RV during sub zero nights. I narrowed it down to the water lines freezing (or partially freezing) in the RV, which caused the water pressure to drop to a very low psi. For whatever reason, when the water pressure is extremely low, the valve on the toilet isn't forced shut, and the low pressure water is allowed to run past the valve, filling the bowl and eventually running into the bathroom.
I did 2 things. Installed a manual shutoff valve on the pex line running to the toilet. I also installed a water leak alarm around the base of the toilet which goes off if the toilet bowl floods.
The RVDreams thread has some good suggestions too. Electric switch, or the electric flush toilet...
Links:
http://www.amazon.com/Honeywell-RWD41-Water-Defense-Sensing/dp/B0049U3XE2/ref=sr_1_4?ie=UTF8&qid=1369182575&sr=8-4&keywords=water+alarmhttp://www.amazon.com/Cash-Acme-22222-Push-Fittings-2-Inch/dp/B000KE4NUO/ref=sr_1_2?s=hi&ie=UTF8&qid=1369182970&sr=1-2&keywords=sharkbite+valve