Actually, no kindles since the first generation have had a user replaceable battery.
Although, as you note, people do it.
My Kindle Keyboard 3G permanently froze about two months ago. After trying and failing with every method of forced reboot I could find on the internet, I decided to do a battery pull, unhooking the battery for about ten minutes. As shown in various YouTube videos, it was easy to gently pry open the case with a small screwdriver. Then it was just of matter of two phillips head screws holding the battery, and, voilą. Went back together fine -- just didn't fix the freeze.
As for buying batteries, go to amazon.com and search for: Kindle replacement battery.
I told Amazon customer service that I had done the battery pull as a last resort. It did not void my warranty.
It is true that the Kindle User's Guide does not explain battery replacement. Maybe this is in the same category as modifying a PC registry. I do that too