Just to followup, I am finding that Youtube, Pandora, and logmein are indeed working fine with Fiddler running, so I'm not sure what the issue was.
I did discover today that if I leave Pandora open for a long time (say 2-3 hours) while paused with Fiddler running, when I come back to unpause, it will usually finish the song fine but generate an error when attempting to load the next song and require Pandora to be reloaded. I don't think it's a session issue because I can typically just refresh the page and it works fine (I have the setting enabled to always keep me logged in). This is on my office computer - on my home computer, I also have Pandora up all the time, and I have noticed that even if I leave it paused overnight, when I come back and resume it works just fine. The only major difference in the two cases is that I run Fiddler on my office computer 24/7, but not on my home computer.
Maybe there's a clue to something about behavior with long-running session and Fiddler?