... now I'm curious and will have to check it out.
Yeah, according to the specs, it's supposed to work like this (quoted from POE Explained - Understanding and using Power over Ethernet):
The final stage after detection and classification of a newly connected device is to enable power: the 48V supply is connected to the cable by the PSE so the PD can operate. Once enabled, the PSE continues to monitor how much electrical current it is delivering to the PD, and will cut the power to the cable if too much, or not enough, power is drawn. This protects the PSE against overload, and ensures that POE is disconnected from the cable if the PD is unplugged.
My guess (and just a guess, based on the outcome) is the PoE injector in question didn't do that and it started lowering the 48V as a result of the increased demand. I suppose it would matter if the heater was inductive or resistive... based on what happened I'd assume it was inductive (heater coils).