Your's is an interesting theory but I can see all sorts of reasons why this never happened. First of all as you point out MS didn't make old Windows 95 code avaailable as Open Source. Secondly, if they had what kind of licensure requirements would they have imposed? None? Somehow I doubt it. Thirdly, what would be the upgrade path? With the linux model life keeps moving forward. With Win95 it would be a technological dead end or it would be whatever Tivo could hack up. Finally, while the gaming angle is intriguing Tivo would never be in a position to be a gaming platform without being very good at their core business. And having linux on their box undoubtedly was a good technological move for their core business - it certainly doesn't seem top have hurt them in any way. For their core business and mission it was probably linux all the way and I bet they aren't sorry. Even if Tivo itself doesn't survive, the name and the concept certainly will and they've had a hell of a good run.
Sony doesn't write all of the games for PlayStation, I'd imagine. Letting 3rd party developers make your games has been a proven money maker for all involved...go with the business model that works...which means that TiVo wouldn't have to do it all by itself.