Who makes up Jokes?

Years ago I read on the Internet that although many people know how to be funny, only professional joke writers create jokes; the rest of us retell their creations. At the time I felt this judgment was too harsh, but each time I actually create a new joke, I wonder if the writer was correct, and I’m one of the elect (I should be so lucky).
It’s interesting to watch how people think when they are actually trying to create humor. Here’s a neat example, at a blog called “I think I want to be a comedian.” A riff on drumsticks.
And here’s a case where I believe the hardworking jokesmith thought of the punchline first.