I've never bought into that theory that runners should continue running after a third out is recorded. After all, OBR 5.07 is pretty clear, in my mind, of what happens:
"When three offensive players are legally put out, that team takes the field and the opposing team becomes the offensive team."
There is no requirement whatsoever specified in the rule that says other runners are required to continue running after "three offensive players are legally put out" to meet whatever obligation they had before that third out. It says that they simply take the field at that point, because all obligations to advance are done, finished, completed.
Obligations to continue advancing to bases after play essentially concludes are limited to when winning runs score. There is nothing in the rules requiring the same after three outs are recorded. So I have no idea why authoritative interpreters out there require runners to keep running after three outs when the rule clearly tells those runner they must now go play defense.