Amazon has been getting into the hardware device category as well as Video distribution through its Amazon Instant Video, and what wouldn't make more sense than bringing TiVo into the fold? TiVo has been struggling to release new features and software updates to their Premiere boxes which were released last year. Those boxes have a dual core processor, but apparently the system is only using one core. We've been waiting ever since the release of the Premiere box to get that second core unlocked, which would enable things like GoogleTV was supposed to, i.e. search while watching video, web browsing, and better streaming web video.
Another reason is TiVo has struggled to make deals with cable companies and other content holders since they believe they lose out ad revenue on commercial skipping used by TiVo. Companies like Comcast and Time Warner cable have bought up a lot of the cable channels and are now large content holders themselves. Amazon already has licensing deals with some of them to distribute TV and movies via their Amazon Instant Video and some free to their Prime members. With the content licensing already in place, Amazon would also have a platform into the consumer in which to sell more Kindle books as well as MP3s and continue to hurt Netflix with their streaming video.
Amazon has more customers than Ebay, and they seem to be loyal. Amazon also has a great backend infrastructure and the technological know-how to make TiVo a better platform than TiVo could ever do on its own.
Just my two cents.