Umpire putting Batter/Runner in jeopardy?

[Dakota]

First of all, I do not have a problem with your statement that it is up to the PU whether to honor the request to go for help. If you know you nailed the call, stand by it. No problem.

I took the OP's question to be asking about whether ASA 10-6-C would apply to this situation. In general, no, it does not (IMO) for the reasons I have already stated.

Your example of the FOUL call that is not a FOUL is not apples and apples, since in the case of the BR, she has a pretty good idea whether or not she checked in time or if she got away with one WRT the PU's call. The runner in your situation has no earthly idea whether or not it was a foul ball. She only has the call from the umpire.

There is also a difference in your "batter is out" scenario in that the PU is emphatically re-emphasizing his call.

I both of those situations, I can see applying 10-6-C to rectify the reversed calls placing the runners in jeopardy.