The answer from the restoration company was: Run both. They use heaters and dehumidifiers.
One person said that heaters actually raise the humidity. That's absolutely correct! Heat increases the convection rate that turns water into vapor, which is the basic definition of humidity.
Dehumidifiers and A/Cs remove vapor from the air and turn it back into water, which you collect - or let run down the side of your RV.
If run just an A/C, you will collect as much water vapor as naturally convects from the water in the wet carpet. Increase the temperature and you generally create more water vapor for the A/C to remove and therefore get faster drying.
If you create heat but don't carry alway the moisture, the vapor eventually converts back to water when it touches a colder surface (condenses) - and hence the possibility of mould in the long term.
It was really pretty obvious :)