According to Percival P. Cassidy :
Let me get this right:
You have CF lamps, unconnected with the garage door unit, that appear to cause problems with the garage door unit, and the problem will "initiate" EVEN IF the CFs are off?
I suppose it's very marginally possible that their assessment is correct, but it shouldn't be that sensitive.
A couple things you could try to rule in/rule out: try putting an optical barrier between the CFs and the GDO, or block off the IR sensor so that it only can "see" the directions where the actuators are. Check to make sure that the CF switching actually switches off the hot, not the neutral. Pull the CFs from their sockets and see if the problem persists.
If it were a classic tube fluorescent, the first thing I'd do is make sure the fixture case was solidly grounded and that it was only the hot being switched.