Class quiz Q

[archangel]

Since this is from a FED class quiz, which has no bearing on the final exams grade, I thought I'd post it for input.

Wilson, with one out and a runner on first base, replaces the starting pitcher Jones in the fifth inning. Wilson, with a legal move, picks off the runner at first base.
A) Wilson may now be legally replaced by another substitute pitcher.
B) Wilson must continue to pitch unless he is incapacitated or guilty of flagrant unsportsmanlike conduct.
The correct answer, from OHSAA test graders, is A.

My question is where can I find this? 2013 Rules, 3-1-2 says "if a pitcher is replaced while on defense, the sub pitcher shall pitch to the batter at bat (or his sub), until batter is put out, reaches base, or 3rd out is made.
2013 Caseook-3.1.2A--- F1 is replaced by S1. Defense wants to intentionally walk batter, then S1 is replaced by S2.
Ruling: Legal, as S1 faced the necessary one batter.

BUT, Batting Rule 7-1-1, Penalties 2, dealing with an appeal of an improper batter , states that the appeal must be made before.......a play or attempted play ...

So, would a pickoff play that would prohibit a defensive appeal on the batter, be the same as the pickoff in the Quiz Q, therefore S1 can be legally subbed for by S2?
Or maybe I'm just overthinking things....