Amazon could probably increase reviews 10 fold by creating an incentive program (e.g., coupon codes for reviewing products).
Or, though it's a little spammy, I wouldn't be opposed to receiving a Netflix/Ebay style email a few weeks after I order a product asking for me to give a star rating on it.
The fact that you're amazed at the outcome is a good indicator that your hypothesis is wrong.
1) They had an exceptional experience with the product and feel the need to react to that. 2) They are the type of person that likes to tell the world about their experiences.
Unfortunately, both of those are a very small subset of total purchases and, most likely, highly overlapping. Which means you won't get the proportionally accurate number of reviews in the middle range. And you won't get reviews from Luddites or online recluses.
If you put an incentive behind the review system, perhaps you'd have people gaming the system, but at least you'd have a better shot at hitting a wider demographic of product reviewers.
You are probably right though. Amazon, like Google, is very, very good at analyzing piles of data to make market decisions. They may well have already piloted review incentives. Regardless, I suspect they've already got numbers that back up their current process.
Another great example of how Amazon has succeeded with user generated content is Listmania--genuinely helpful product lists, all provided for free. I don't completely understand the psychology of why these are created, but I value the content greatly because I know that contributors are not compensated for their suggestions.
I'm a heavy user of Amazon in the UK (Prime membership and all), and I get regular emails asking me to review products I've previously purchased.
..I've never written a review, though.