In my opinion the name refers to the amount of turn the man does: up to a 1/1 made "all at once", asuming that the rotation startet with the spin is continued fluently with the toe pivot.
The highest amount of turn in other movements is 1/2 ('pivot'; 1-3 of V. Waltz/Rev.T.) so: at the Double Reverse Spin man dance "double" of normal figures. On the other hand perhaps one day the name could be changed, because there is no other Reverse Spin (it sometimes happens, like "Overturned Turning Lock -> Turning Lock to R").

About pivots: Turning to R: Natural Pivot (bwd step), Pivoting Action (fwd step). Turning to L: Reverse Pivot (fwd or bwd), Toe Pivot, Heel Pivot (former ending of Quarter Turns + Chassé Rev. Turn in Quicktep)
They all have in common: turn is made on one leg AND if it was a bwd step it's followed by a fwd step and vice versa (Swivles are similar but are followed by a fwd step if fwd ...)
Interesting question: in some figures both partners seem to have pivots "at the same time", but that's physically impossible, because the couple is ONE OBJECT, that can't rotate around two parallel axises. Solution: even if the pivots are at the same step#, the axis of the couple changes from man's to lady's foot (i.e. Nat. Pivot Turn) or vice versa (i.e. Reverse Pivot)

Nothing funny about this step Double Reverse Wing. Steps are pretty much as in the Double Reverse Spin except the lady has to finish on the mans left side as in a Wing. The man's next step is outside the lady on her left side. Not for the faint hearted.

Here,here,here!.!. Arent we all forgetting what we had previously opined about?? That being good basics. If we teach and adhere to good basics, then any variation (Pattern) is simply a different spin (Scuse the pun) on the basics to begin with. Inside, outside and heel vs ball are all taught to begin with so, "If you dare" shouldnt be a concern at all but simply "Here's the footwork now go do it but remember the basics"