I would like to agree, but the Casebook plays do "fix" situations where there was no umpire error.
10.2.3 SITUATION H: With a count of three balls and two strikes on B2 and R1
on first base, the batter takes what appears to be a half swing. The plate umpire
calls ball four and R1, upon hearing ball four, then trots to second base. The
catcher throws the ball to F4 who tags R1 before he reaches base. The catcher
asks the plate umpire to check with the base umpire to see if B2 did, in fact,
attempt to hit the pitch. The base umpire indicates that the batter did swing at the
ball. RULING: The plate umpire will declare the batter out and return R1 to first
base. The umpire-in-chief can rectify any situation in which an umpire’s decision
that was reversed has placed a base runner in jeopardy.
10.2.3 SITUATION I: With a count of three balls and two strikes on B1 and no
runners on base, the pitch is made and the batter takes what appears to be a half
swing. The plate umpire calls ball four as the ball gets away from F2. B1 trots to
first base and F2 throws the ball to F3, who tags B1 prior to his reaching the base.
F2 asks the plate umpire to check with the base umpire to see if it was a strike.
The base umpire indicates that B1 did swing at the ball. RULING: If, in the judg-
ment of the umpire-in-chief, B1 would have reached first base before the throw if
it had not been called ball four, the plate umpire can award B1 first base. The
umpire-in-chief can rectify any situation in which an umpire’s decision has placed
a batter-runner in jeopardy. Advances and outs made by runners following a
reversed call stand, if the call that was changed clearly did not place them in
jeopardy.
On the other hand, for umpire mistakes involving the infield fly rule, the players are all supposed to know the situation, and the results stand in FED.
IMO, FED rules and casebook plays sometimes lack consistency.
All these case plays refer to a runner in jeopardy. That is not the case in the OP.