In fact you just need one of the two ends to be able to auto swap RX/TX.
But GigE uses all four pairs, so the hardware has transceivers behind all four pairs, which means even when they're running at 10 or 100, the chipset can choose which pairs to transmit and receive on. Thus all GigE adapters are Auto-MDIX, and it meant I no longer needed to carry a crossover cable, no matter what other device I was talking to.
It's funny how 10/100 cards with Auto-MDIX capability were exotic and expensive, but once GigE had it by default, it became ubiquitous, cheap, and quickly forgotten.