I think that's what this part means -
Purl to the end of the row, but before purling the final stitch, pick up the next purl bump from the hem, and purl with the final stitch. (This smoothes the transition from the brim to the hat.)
And later - Purl to end of the row, once again picking up a purl bump and knitting it with the final stitch. Knit a row, pick up a purl bump and knit it with the stitch. Bind off in purl."
That sounds to me like you're going to do a p2tog using a stitch from the brim and where you switched to purl on the RS. That will have the effect of rolling the brim and joining the edge where it started.
sue- knitting heretic