Here I'm having a look at the YouTube app for Virgin Media TV powered by TiVo. As you can see I'm searching YouTube (for one of my previous TiVo videos actually!) and the result shows up, I assume the standard quality for that video is chosen by default, and I didn't see a way of choosing other quality settings. Someone asked me to answer that question on the TiVo Community
Enjoy! please feel free to ask me questions in the comments and when I can get the remote from the wife I will try to answer questions!
For a bit of further reading on the YouTube integration check out this link