Here is a 20A, 250V receptacle (6-20R):
In my house, there is one that was wired using "BX" 10-3. (It's either type AC or type MC, black/red/white, no separate ground conductor.) At the device, the black and red connect to the two hot terminals, respectively. The white connects to the ground terminal.
At the panel, the black and red connect to two 20A breakers, with the common trip (is that the term?) so if one trips, the other does as well. The white is connected to the neutral bus bar.
Do you see any problem with this?