Len Scrivener's book was published in 1951, ten years before Wally's, but that is irrelevant.
In your first post you said "there is a hip movement to the ladies right on 4 1 which will without trying, turn her an 1/8 of a turn to her left". That makes the turn part of step 3 not step 4.
You later say "Where did you get turning too early from. How much later than beat one can it be." Try beat 2.
In your latest post, "Do they actually turn at the end of step 3 which is the beginning of step 4 or do they turn at the end of step 4." The end of step 3 comes before the beginning of step 4 although admittedly not by much, but I see you now say that the turn happens directly after step 3. This would tie in with the man's turn which is also on step 4 and not pre-empted by turn at the end of step 3.
The original question was why was the lady's 1/8 turn not described as a fwd walk turning. As I said earlier, the most recent manuals don't seem to use the term, but the ISTD (1998) using their study alignment as reference make the turn later in step 4, very similar to a fwd walk turning,
"4 (LF fwd) against LOD to end DW against LOD"
And yes, I do see it danced and demonstrated that way.