slacker is right about HD Tivo not doing native resolution as long as you agree to the definition of 'native resolution'; let's have a semantic debate!
More often and perhaps (no offense, slacker) more accurately referred to as 'native pass-through', 'native resolution' is a setting that ALWAYS passes the original signal's resolution through unconverted: if it's Discovery HD it is output at 1080i; change to ESPN HD and it is output at 720p, all without changing any settings on your STB.
Now with the HD Tivo (which I also have), you can change the ouput resolution, but every channel is then output at that resolution regardless of the original signal resolution. You can set the HD Tivo to always output to your TV's native resolution, as I do, but you cannot have the HD Tivo always, regardless of what channel you are on, output the native resolution of the original channel.
This is considered by many enthusiasts to be a real flaw in the HD Tivo, and they are constantly agitating for Tivo to fix this 'flaw'.
When I discussed in my previous post how I tried outputting the unconverted signal from the HD Tivo to let my TV do the conversion, that actually meant that for each individual channel I had to know what the native resolution was, and whenever I tuned to that channel I then set my HD Tivo to output that resolution so that it wouldn't be converted. Tedious. Fortunately, since I saw no picture quality improvement, I went back to the always-720p output setting for the HD Tivo.
--Dino