Any chance your MRF/RFX setup is set to channel 0?
If so, a neighbor's remote could be jamming you.
As mentioned above, set the base station to different channels to see if the ghosts go away.
Also... A ferrite filter on the antenna was a solution mentioned in the past for URC MRF issues.
I'm Not an engineer, but I play one on TV. My handle is Tweety but I have nothing to do with the organization of similar name. I just had a really big head as a child so folks called me tweety bird.