The Backwards Loop Cast On is found of page 66 of RD KH (titled “Twisted loop cast-on”).
You can find a video of this cast on on KnittingHelp.com, titled “Single Cast-On.” You can also see an illustration on TECHknitting, under “Casting On by ‘Looping On’ method” (It is the third illustration in the post.)
The backwards loop cast on is done with one strand of yarn and one needle. It isn’t nearly as stretchy as the loop cast on, and is IMO not very pretty. It also wasn’t very much fun to knit the first row, the stitches wanted to fall off or had weird tension. The double row of twists at the bottom looks kind of cool and could be used as a design feature.