[greymule]

It's true that a runner who continues to run after being put out "shall not by that act alone be considered as confusing, hindering or impeding the fielders."

I would apply "not by that act alone" to mistaken running after an uncaught third strike, to routine rounding of 1B after a fly ball is caught, to continuing to run toward 2B after a force out, and to other cases in which the runner can't be expected to disappear or stop dead. But I wouldn't interpret those words to mean that the runner has license to deliberately confuse the fielders.

In the OP, no interference. But:

Bases loaded, 1 out. Strike 3 gets by F2 and caroms off the backstop toward the 1B dugout. Umpire announces, "Batter's out!" but the BR runs anyway. As F2 chases down the ball, R3 scores, R2 scores, and R1 takes a big turn around 3B. The BR rounds 2B and continues toward 3B. As R1 returns to 3B, the BR stands halfway between 2B and 3B trying to get the defense to play on him. The defense then plays on the BR, who gets himself caught in a rundown while R1 looks for an opportunity to score.

I think that qualifies as INT on the BR, even though you could argue that the defense should know that he was already out.