It sounds like it should work out as written. I worked it out on paper and it works. The first decrease row is crown row 1. It will be K1, p1, k1, p1, k1, p1, k1, p1, then k2tog, and repeat that across. Because it is knit 1, purl 1 all the time it works out on row one of the crown that the first K2tog uses up both a knit and a purl so that the next stitch in the sequence is another k to start the next sequence.
On row 3 what they give works out correctly. K1, p1, k1, p1, k1, p1 and then you have one more k1, p1 presenting themselves before you. Knit only the first one and then you have a purl and one stitch where you worked the two together in row 1. You purl those 2 tog and then you are ready to start that sequence over again.
So just follow the pattern very carefully, exactly as it says. It is correct.
what does it mean to"purl the knit stitches and knit the purl stitches"?
To create seed stitch you always do just the opposite of what presents itself to you in a row. You know how when you do a regular knit row in stockinette stitch (where you knit a row and purl a row) that if the row has the purl bumps face up as you begin the row that you purl that row (purl the purls)? And if the smooth side with the "vees" are face up as you begin a row that you knit that row (knit the knits)? Well, with seed stitch every other stitch is different, k1, p1, k1, p1 all the time, but on each row after the first if the stitch next on the needle is a purl bump facing you, you will knit it (knit the purls), and if a smooth 'vee' is facing you as the next stitch you purl it (purl the knits). It sounds complicated, but it isn't just do the opposite of what the stitch is as it faces you.
I hope this makes sense.