Yes, yes. Of course we need to think about what we are saying and
about what we might accidentally be saying in any given written
passage. And we must insure that unintended meanings are avoided.
On the other hand, we must assume at least a little intelligence and common sense in the reader.
No reasonable person would ever think Nixon was going to resign because
someone's sister worked in the White House, for heaven's sake!
(Nevertheless, I do agree that the comma helps in this case.)
CJ