Power supply voltage problem

My internet router stopped working. No power supply light, dead, nada. It has a plugpack power supply. First thing I checked was the voltage on the plug from the supply. 5v exactly as it should be. I called up the support line and they said “probably a dud plugpack, we’ll send you a new one” I said “nope don’t think so, it’s still showing the right voltage”. They said, “well we’ll send you one anyway, because you never know”. Whatever.

So they send it out and it works. Clearly the old plugpack was the problem. What’s going on here? By its size and weight it’s a switchmode transformer. Could it be capable of outputting a nominal voltage (sufficient to fool my multimeter) while not actually capable of maintaining even enough current to light the power supply LED on the router (not even with any load on)?

Or what?

Yes. Power supply regulation must be tested under load.