mbyron,
Good ol' caseplay 8.2.3 is still in the book. It first appeared in 2005, and was widely believed to be in error and would be revised. So far it hasn't been.
8.2.3 SITUATION: B1 hits a slow roller to F5 and arrives safely but misses first base. F3 catches the ball with his foot off the base and casually steps on first base, though he believes the runner has beaten the throw. RULING: B1 is out. Because a force play is being made on the runner and is the result of continuing action, F3 is required to appeal the missed base and does so by stepping on the missed base.
See
Accidental appeal and mechanics question. for an example thread.
For any reader here who wishes to argue that a runner can't be forced to first, see the wrangling in the above thread, and then please ignore the issue. It isn't central to the current topic.
Anyway, 8.2.3 is the basis for the ruling in the BRD.
ETA: Actually, 8-4-2(i) is cited as the basis for the ruling; 8.2.3 is simply related. Childress claims that accidental appeals have been abolished, but not accidental outs.
Any runner is out if he:
"i. does not retouch his base before a fielder tags him out or holds the ball while touching such base after any situation (
8-2-1, 2-3 and 4). Umpire may also call him out at end of playing action upon proper and successful appeal."
8-2-1 "An advancing runner shall touch first, second, third and then home plate in order, including awarded bases."
Personally, I am not convinced that CC is correct.