If I were betting, I'd put my money on it being a neighbor with X10.
HouseCode "A" is the default that all modules come on from the factory, and many people don't bother to change it. That is the whole reason why they developed it with a separate "House" code, the idea being that each house on the pole transformer would be set to its own code, thereby eliminating interference from one house to another.
You never changed your HouseCode from "A" to something else, and you probably have a neighbor who never did, either.
since changing the Housecode takes almost no effort (you may have to open up the electrical boxes to get to the dials on the XPFM modules, though), that is probably the fastest route.
As for the reason your lights would sometimes go right back on after being turned off, if your neighbor's signals are entering your house, chances are the same is happening in reverse. When you turn off your A1 light, his goes off, too. He doesn't like sitting in the dark, so he turns it back on.
If you have either a CM15A or CM11A computer interface with the software, you can monitor what's going on more easily.