So, the new TiVo does
have a Bluetooth receiver, just not built-in WiFi. Given the thumbboard, there are so many codes on that remote that it might have been difficult to do with IR. Also, holding the remote such that an IR emitter is always pointed at the TiVo while you use the thumbboard might be challenging.
The PS3 remote is Bluetooth with no IR receiver--very annoying to many PS3 owners who use universal remotes. Logitech introduced their Harmony® Adapter for PLAYSTATION®3
and solved the problem for me. The adapter is connected to nothing other than power; it receives IR commands and translates them into Bluetooth commands. (Before the Logitech solution there were many tiny little companies selling stuff, some of it in some ways superior, but I trust Logitech).