I am pretty sure I know what she is talking about.
First, to understand the two terms, let’s quickly define both.
Slip stitch: moving a stitch from the left needle to the right needle without working it. (Do not knit or purl, slip as if to purl)
Double Knit: Fabric that is double thickness, showing knit stitches on both sides. Amy shows one form of double knitting here but this is a slightly different method than what you are going to be doing. In Amy’s example, she works in two colors, knitting both sides of the fabric in a single row, then turning, switching the colors and knitting the remaining stitches on both sides of the fabric.
In the method for the scarf, you will use only one color and knit the front of the border on one row and the back of the border on the return row.
A slip stitch double-knit border is made up of three stitches at each end, so add a total of 6 stitches to your pattern. I like to place a stitch marker three stitches in at each side, to remind me that those stitches are extra–separate from the pattern itself.
On all right side rows: K1, sl1, k1, slip marker, work pattern to last 3 stitches, slip marker, k1, sl1, k1
On all wrong side rows: sl1, k1, sl1, slip marker, work pattern to last 3 stitches, slip marker, sl1, k1, sl1
Note that the border stitches are always knit, never purled.