Auto MDI/MDI-X + conference rooms + bored == loop

Can someone please explain how can the whole MDI vs. MDI-X distinction
be meaningful at all for 1000BaseT? I thought they run 250 Mbps on each
of the 4 pairs in both directions using some form of echo-cancelling
hybrid techniques. If one no longer has separate Rx and Tx pins, how is
it meaningful to talk about MDI or MDI-X?

I thought that for 1000BaseT a straight-through cable was always the
"native" cable choice for connecting any two ports, be they switch ports
or station ports - is that not true? It also seems to me that a
crossover cable should never make sense for 1000BaseT, but from what I
understand such cables do work because the PHYs are generally smart
enough to detect "hey, I'm seeing signal on pair B that ought to be on
pair C" and auto-correct.