"On 6th row, K 45, BO 13, K 4, turn and K back 4, repeat, BO 13, K across"
For the 6th row, I think you do need the turn in order to put in the extra rows between the eye openings. The directions aren't completely clear but it seems to me that you
On 6th row, K 45, BO 13 (eye #1), K 4, turn and K back 4 (on the WS), repeat (that is, turn and k4 on the RS), BO 13 (eye #2), K across (to the end of the row).
I agree that for the next row, the "Continuing.." instructions, there's no turn.