Both of these videos depict exactly what I (and the guy I quoted) described. What don't you get?
There is no inversion (inversion meaning feet go overhead) in a flat spin.
Another way to think of it, would be a 1/4 of a lincoln (so that you'd be parallel to the ground), a "backflip" (while laying on your side, so your feet never go over your head), then coming back on axis.
Obviously it's not as cut and dry, because it's a smooth trick and the parts are not nearly a cleanly separate, but that's the idea.
As far as I'm concerned, there's almost no such thing as a "flat 3". I think that what most people refer to as a flat 3 is simply a barely off axis backflip (almost a 45 degree backflip). I have seen a few truly flat 3's, but I can count them on one hand. I believe Andy Mahre does a really great one.
Though flat 5s and rodeo 5s are thrown differently (depending on who you ask), they can often look very similar, and the only true difference visually is that at some point during a rodeo, your feet are higher than your head.
Now, this sparks a whole new controversy as a "new rodeo" has emerged where there is no true inversion. Good examples are McChesney (particularly rodeo 9 and up) and Matt Walker. In my opinion, they're basically doing old school bios (that look a lot like CR's from Ski Movie 3). If you watch them, they're basically doing an upright slightly off axis rotation in which they're "leaning" downhill towards the landing. EXAMPLE: Rodeo 12 at 1:02
The whole naming and describing tricks phenomenon has become incredibly subjective and confusing.