From the sound of it, it just sounds like you need 100% cotton yarn, nothing else, plus with the finishing directions ("Weave in all yarn tails to wrong side of work. Block. Pin edging to 1 end of towel; thread sewing needle with matching thread, and attach edging to towel with overcast stitch. Remove all pins."), you're sewing the newly knitted yarn to the fabric of the towel.
That's my understanding. I could be wrong.
ETA: I'd wait to see what someone else says before listening to me. I started a few weeks ago, and might not know all the knitting secrets.