The Mystery of the Ghost Calls

Incoming faxes are disabled (fax doesn't work with the answering machine because they are on different floors) and machine is turned off, although still plugged into the phone line. It is not a smoke detector or low phone battery. The batteries are new, fully charged and the handsets are always in the cradles when not in use. I was not asleep (A couple of times it occurred in the morning and I was near the phone when it rang). The power lines are not buried, but are above ground and come in on the same poles as the phone lines. I have not had any power issues lately, although fluctuations are not uncommon out here in the foothills. Up until recently, the problem didn't exist, which may suggest some failing component, but it is very intermittent, which means the problem may be difficult to troubleshoot, to say the least. The question remains though: how can the ringer operate if it is turned off: intermittent short in the phone?