I think I'm getting the idea. Seems like she made a typo because it says to purl on the knit side and vice versa where the photo doesn't look like that's what she did. I just switched them around, though...easy enough. Here's where I get confused. After doing the short rows for the bill, it directs you as follows:
"Continue in the pattern established, wrapping and turning stitches earlier each row until you find yourself knitting fewer than 26 stitches in a row.
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.)
Turn work. (You are now working reverse stockinette. This will curl to the underside of the hat and look like a corded edge after you felt the hat.) 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."
So, by reading the bold part I can't understand...does it matter if I end on a knit row or purl row?