The above doc outlines the potential for a minor confusion between us audio geeks and the transmitter guys. Yes, dBm is a power measurement where 0dBm = 1 mW. In transmitter land, this is referenced to 50 ohms, which gives a voltage level of .224V. In our biz, we reference to 600 ohms, giving a voltage level of .775V. We arbitrarily call this voltage 0dBu, since dBm is meaningful only in the power domain, and the notion of 600 ohm transmission lines is obsolete in our world.
To be explicit, one should probably always express the reference impedance for power measurements like this: dBm(50), or dBm(600) as I agree there could be confusion otherwise. Especially if you are willing to admit there are industries other than audio in the world.
Just as an aside, there is actually no such thing as a true transmission line in audio. This is something the phone company has to worry about, but unless your tie-lines are greater than, say, 5 miles it's just a wire with lumped parameters.