I'm outside my comfort zone talking about this and hope someone can help us out, but I suspect the volume control is not a comprehensive gauge of power requirements or if the amp is struggling.
I would bet a cheap AVR would die pretty quick with a 3 ohm load. I believe this could happen at -20dB. That doesn't mean it could not play loudly as it fried.
My brother has destroyed the amp sections of a Yamaha RX-797, Onkyo TX-8555, and a Carver TFM-15CB amplifier, by driving too low of an impedance. According to him, they sounded fine until they suddenly cut out.
Now hopefully someone will come along and illuminate us!