No need to apologize for being hard headed, you obviously want to understand. While what you are looking for may not be spelled out, you can use the rules and reasoning to get "the spirit of the rule" .
My contention is the BR being thrown out at first is an appeal play.
If a runner leaves 1B early on a fly ball to right which is caught, and is thrown out at 1B this is a "live ball appeal". Why was the runner out? because she was "forced" to return to 1B, and the defense properly executed a play on her. If another runner had crossed the plate, and this was the third out, that run would not score. I doubt anyone will argue that.
What is the difference then in the BR being "forced" to touch 1B? The defense makes a proper appeal by making a play, and thus you have the 4th out negating the run.
The way the rule is written may be misleading if you let it, (such as the D3K rule which allows a runner to run on a D3K with 2 outs, only if 1B is occupied, if the base is open and two outs, well...).
I believe the intent of the rule (5-5, and POE 1-J) is to judge when a run scores on a "timing play" rather than to allow a run to score in this instance.
Also, not that this would make it right or wrong, but if you were to disallow the run on the field, I doubt there would be any arguement whatsoever. If you declared "run scores"...........
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