Knitting: How does drop stitch edging hide color changes in a striped scarf?

I read these instructions for how to make this pretty scarf, and I’ve got most of it down. The only thing i don’t understand is how to hide the color changes.

Basically this part:

On scarves of this nature I prefer to work a slipped stitch edging which adds a nice, polished touch and perfectly hides the working yarn as you carry it up the sides whilst striping to your heart’s content. I worked two-row stripes using two different colorways of Silk Garden, slipping (purlwise) the first and last stitch on the second row of every stripe.

On the swatch I’ve been practicing, the color changes are not “perfectly hidden” there’s one suspicious line of the opposite color visible in each row.

What I’ve been doing is: Knit two rows with color 1, by starting the first row with a slip stitch (purlwise), then doing the 1×1 rib, until the last stitch of the row, which I knit. Then I switch to color 1, knit two rows of that the same way, then when I get back to where I was, I just pick up color 1 again, which creates the suspicious line.

Maybe I just don’t understand how to “weave as you go”. I read this definition of it, and to me, it sounded like exactly what I was doing, but maybe it’s not? Should I be knitting with both colors on the needle together all along one side of the piece?

Can you explain to me, step-by-step, what I should be doing?

Also, please keep in mind, when answering, that this being a scarf, there is no “front” and “back” and I wouldn’t want to create a defined front and back

Thank you!