I don't know why it's called a noid light, but one concern with using a voltmeter is it won't respond fast enough, typically. The injectors fire with a pretty short pulse width (milliseconds) which is pretty hard to measure with a meter. You may be able to see the meter display move, but you wouldn't be able to get a good feel for amplitude. If there is a loose or corroded connection somewhere in the system, amplitude could be pretty important in diagnosing an injector issue. A shorted or nearly shorted injector could be pulling the signal low, but with a meter you'd never see that. Of course, since you unplug the injector and put a noid light in its place, you wouldn't see that with a noid light either. That's one of the reasons I back-probe the injectors and use an oscilloscope. That and I don't own a noid light set.
I've wondered why it's called a noid light too, but never seeked an answer. Maybe they were eating Dominos pizza when they developed the light.
-Rod