I found the pattern for "The simplest cap of all", and it is knit in the round, so instead of knitting a row, turning and purling back the other side, you just keep knitting in a spiral for as long as you want it to be. It is stockinette stitch ( smooth knit stitches on the outside, purl bumps on the inside) but made without any purling.
If you did a round of knit stitches and then a round of purl stitches, you would have garter stitch, even though, as you said, garter stitch is "knit every row" if you were working back and forth on a flat piece.
There is really no error in her pattern, just an assumption on her part that the knitter has some basic knowledge. The designer assumes that you know the difference between knitting flat and knitting in the round, and now you do.