By logic, you are saying Fred Thompson would have championed Ruth Bader Ginsberg.
Hardly. Darth Vader Ginsburg was appointed by a Democrat.
It is a matter of fact that moderates from both sides shepherd their respective appointees through the process. How would you expect someone from the hard right camp to have any influence over the left (and visa-versa)?
It is not in Thompson's favor that he was such, or at least not if he is supposed to be a Conservative.