Your friend is correct. If he disconnects his ground detector(s), he should get different results, ideally zero volts.
You don't want them to add up because there is not supposed to be any connection to ground. I don't really like the terms, "phantom" or "ghost" when discussing voltages. We did have a ghost at WCLQ-TV in Cleveland, but that's a completely different story. My original saying is, "All the world's a voltage divider." Your DMM probably has an input impedance of around 10 Megohm. A VOM could be around 50Kohm/volt. For kicks and giggles, connect your VOM and DMM, both on AC volts, in series across your transformer. The voltages that you observe on both, should reflect the ratio of their input impedances. You might not see much on your Weston, while observing almost full voltage on your DMM.
So if you hook your 10 Mohm DMM up to one leg and ground, and read about 60 volts, you are probably dealing with about a 10 Mohm combination of resistive leakage, and/or capacitive, and/or inductive coupling.
Joe