I really doubt they were stealing jokes(especially considering the 2 are made so long apart). The first part is simply something which is more or less normal(at least in my experience), with parents talking to you about someone you might have known when you were a little kid 10-20 years+ ago. And the punchline is simply an easy conclusion way to mock it.

So I can easily see 2 different people come up eith 2 similar jokes

Isn't this a plot to a studio 60 episode?

As I have experienced this in real life, and seen it in quite a few sitcoms/movies, I don't really think this is an uncommon joke. 

Ouch. Someone on the writing staff is stealing jokes!