I have not tested with IE7 yet, so I can only go by what is posted in the forums and personal conversations I have had with users. But to the best of my knowledge, the software is compatible with IE7, it's just that the various configuration settings that IE7 sets by default prevents the software from functioning properly. So, the basic idea is that you flip a few switches and the TD should work with IE7. I just haven't worked through the process of identifying what those switches are.
Theoretically, you could flip the same switches with IE6 and see the same situation, in that the TD will stop functioning. It's just that Microsoft didn't configure IE6 that way by default, as they are doing with IE7.
Firefox, or any other browser really doesn't have anything to do with it. I personally use Firefox. All the TD needs is for IE6 to be installed.