I have no idea and it sounds like everyone is guessing. I don't know why the designer didn't explain what she had in mind since she was inventing a new abbreviation.
This hat is a bit of a mystery because you can't do a cable around your head without working it first over a few stitches and then joining it into a band and picking up stitches to continue the hat. Nevertheless the designer says nothing about anything of the sort. I think she has devised some way to do the impossible. :-) (this happens in knitting) LOL
In the quote above, that was someones interpretation of what she may have meant and what she apparently did; it sounds like all she is saying is that the PS is slipping a stitch purl wise.
Is she simply slipping the stitch, untouched, from the left needle to the right?
That seems to be what she is saying. If so why didn't the designer just say so; there is a standard abbreviation for a sl st?
Insert your needle as though you were going to purl the stitch, but just slide it unworked to the right hand needle. Give it a shot and see what happens. You will probably have to do quite a bit to really see what is happening if anything.
I think I would find another pattern. LOL