Perhaps one reason why they ask puzzle type questions is because they don't care so much about what content you know. You can learn on the job after all if you are smart.
But that still ignores the issue about whether puzzle solving and programming ability are highly correlated.
Probably moreso than most other things you could evaluate, including programming itself. I'd argue that puzzle-solving is more closely related to what you actually do as a developer than writing "reverse a string in-place" exercises in C. After all, what are programming problems besides puzzles?
(Assuming you're working at a firm that actually develops software, instead of handing a template to some code-monkeys and telling them to use off-the-shelf Microsoft or Java widgets and assemble them into something vaguely resemblant. But the latter firms don't really use puzzles anyway. They hire based on degrees and certifications.)
The point is this is just a guess. You need scientific experiments to demonstrate this -- otherwise, it's potentially illegal to use puzzles in interviews.
A guess seems like a reasonable standard of proof, the experiment is when you hire them for a month to see if they can do the job. If that's illegal then the laws are broken.
But that still ignores the issue about whether puzzle solving and programming ability are highly correlated.