Haha I see this is a controversial topic!
The debate about whether or not you are truly ever flat basing is semi-legitimate, but the "no true snowboarder would ever do this" comments we can do without I think.
It's obviously not physics defying to do it. On a perfectly flat slope with a perfectly balanced snowboard and perfect snow, aimed perfectly down the hill, the snowboard will go down without catching an edge. Whether it's practical to do this in the real world, and for how long, I'm not qualified to say.
I'm a little skeptical of the school of thought that people who are "flat basing" are always on some edge, even if only slightly, but maybe that is the case. The main reason I am skeptical is because I've seen them do this on the hill in a straight line and I've seen the tracks it left. Favoring any edge will cause drift. I didn't actually measure, so maybe they drift ever so slightly proportionate to them using an edge ever so slightly, but it sure seems like people have periods of flat base riding as appropriate.
As for bordercross, except when popping off of the lip of a jump, bordercross racers are generally carving. A carved turn will actually accelerate the rider where as a flat based skidding turn slows the rider. To win, these guys want speed and are carving not flat basing.
In turns, yes, definitely they don't want skidding. However, during any flat sections, they want the most direct line possible. If they have a direct, optimal line for a section of the course, I can't imagine that they are going to deviate from that path whatsoever just to use an edge. The only way to go perfectly straight is to be flat. If you're turning at all, you don't want flat, as that will skid, as you say. But when going straight, flat is faster. Think about it, you have a direct line, you are going to turn or veer unnecessarily and waste precious tenths of a second to avoid an edge catch? Gold medal on the line?
I have no experience with that obviously, but thinking logically, observing them, and considering basic physics, you're saying they're never actually flat? If you are sure of that, I'll defer to your expertise, but that would definitely surprise me.