Is ball "dead" after 3 outs... Situation

[DDonnelly19]

How about the adventageous "5th out?"

Bases loaded, 2 out. Popup to F6. R3 breaks for home on contact; R2 holds near 2B, thinking there's 1 out. R1 breaks for 2B. F6 drops the ball. R1 passes R2, but after R3 scores. 3 outs. R2 then is put out while trying to dive back to 2B. 4 outs. Now the defense realizes that the BR has stopped on his way to 1B, thinking the play is over. Ball thrown to 1B, and the BR is out at 1B, therefore cancelling the run on the advantageous "5th out."

Here's what I don't understand -- is J/R advocating keeping the ball live after the 3th out, so that the defense may have a chance to cancel any run scored during the play? In the example given, the BR injured himself on his way to 1B, so is J/R saying that this special circumstance (runner is incapacitated before the 3rd out is made) allows the 4th out to be made?