I always understood this rumor of Paul being dead as having started from that bit of backmasking in the Beatles recording, where, when you played it backwards, it said, "Paul is dead". Then the phenomenon ensued where the fans went crazy with it, and thought Paul was replaced by a robot or whatever. My impression of the whole thing is more as just a random, weird, thing that happened.
Later on, a bit of comical backmasking was worked into an episode of GI Joe, probably inspired by the Beatles:
https://www.youtube.com/watch?v=bH94U2-0VCY