I think it is a matter of personal choice of equipment, as for as the DMM, Solenoid debate goes. Both have benifits, and draw backs.
A lot of things I cant do with a wiggy, but dont reffer to a potential seen on a meter as "Phantom or Ghost", IMO belief in such things in that context can only lead to trouble. It may not be usable under even the smallest load, but it is there. Likewise, just because a solinoid is popped up in a certain range, there is a big difference in 120 vs. 150v or 90v that is not totally obvious on a Wiggy. Both instruments are subject to interpitation to some degree. But whatever the choice in tool is, you need to know the limitations of it. I have a Fluke 322 that I use for most things, it does the job, and I like the way it does it. Not to look cool.
On the original question, "One, is that the voltage is being induced on the wire. The other is that at least two circuits are sharing a neutral and the voltage is being back-fed. What do you think???"
Could be either, depending on the circuit and layout of it, and what it is measured against.
"I still get about 15 Volts coming through to the outlet in the ceiling when changing a light or ceiling fan. When the circuit breaker is turned off, the voltage drops to zero."
15volts is obviously not a usable voltage for the intended circuit, but does not mean it is not there. Think about the circuit path, where you are measuring you could be about 100' from the panel. Wind all that wire into some neat coils and you could end up with more, and it could be usable to boot.
