I don't think that the tape loop does the deed at all. The purpose of a buffer, be it tube, or transistor, is to present the driving load with a very high input impedance to take the current demand off of the wimpy output stages in inexpensive CD players, DVD's, etc, resulting in inproved dynamics and frequency response. The second half of the equation is that a tube buffer will have a very low output impedance to drive long cables or hard loads.
If you put the buffer in the tape loop, the CD player will probably see the input impedance of the preamp section which will not really help the dynamics and frequency response of the Music Hall. On the other hand, if you are just buying the device to get some fattening from the low order even harmonic distortion of tubes, then the tape loop is fine. Of course, as with all things audio, this is in the ear of the beholder and you are free to try both ways.