The current iteration of the rumor comes from the blog The Technum. Someone did a simple straight line extrapolation based on when Amazon reduced the price of the Kindle, and came to the conclusion that the Kindle would be free by November. I embedded the chart above so you can see it for yourself.
A straight line extrapolation works for math but it does not work when you factor in human behavior.
I don't believe this rumor; if Amazon did this they'd lose money. One justification given for this rumor is that whatever Amazon loses on hardware sales they'll make up on ebook sales. That might be true now, yes. But you don't know tat it will be true when the price is zero. I think the average is about 10 per ereader owner per year, and that's not enough to cover the cost of a $190 ereader. Besides, most heavy readers already have an ereader. A free Kindle would pick up the fringe cases, not the heavy users.