Mount it from the inside you lose resonance.
Mount it from the outside you are putting additional stress on the tuning lugs its attached to, which will put your drum out of tune easier.
I guess i still dont see the point, unless you're looking for absolute precise repeatability every single time you mic the drum. In which case you could still get the same results using a stand, and you don't have to worry about breaking this thing bolted to your drum.