I just replaced an old digital thermostat with a new programmable honeywell. The wires coming out of the wall are as follows:

In the old thermostat they were connected as follows:
Red:Rh (jumpered to RC)

The unit is a gas heater/AC unit. I called honeywell about this but just want to double check. The new honeywell unit does not have an RH or RC terminal, just an R. Honeywell told me that I don't have to jumper in this new unit because just plugging the red wire into the R terminal will take care of it. They said it would only be problematic if I had separate wires coming into the house to the RH and RC terminals. The heat is running fine right now so I feel they are correct. Do I need to just put the old unit back up or are they correct?