Think about it this way though ... you don't know, at the moment the 3rd out was made, whether the batter-runner would have been safe at first... but once that 3rd out is made, they have no reason to continue running, so you'll never really know.
The rules make it easy for us in just about every case. If the 3rd out is made on a batter runner before they reach first, or on a forced runner, no runs can score. In any other case, runs that happen before the 3rd out count. (And a polite request for the umpire lawyers to not confuse the situations with extraneous info that doesn't apply to OP's situation! Please!?!?!
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