At the same volume? I certainly accept that the sound signature can shift as new gear is used, but it won't change the sound signature of the headphone significantly, that really isn't scientifically possible, unless the two amps/amp + DACs being compared are very different sounding to begin with, and or, if one of the amps and DAC devices is really poorly designed. Don't forget, the majority of amps for instance, even very inexpensive ones, actually have distortion ratings well below the point of practical audibility. Really nasty ones when pushed and with a load will certainly introduce some audible distortion, but that isn't as common a reality as we might expect. The P9 sounded pretty nice from my G4, albeit too quiet for my preferences.
Now I can really accept more clarity being introduced by a better DAC, that isn't so hard to accept, but that isn't what was being discussed. The idea was that the P9 requires more power to start to be itself, but the reality is that the P9 is extremely easy to drive. Yes, I can agree with you that some improvement is possible with a better amp as they can handle the frequency response swings better and help control the driver, but again, unless the other amp was extremely bad at this, you aren't getting significant changes simply from adding a little more power which is what has been suggested. You may get minor changes, but we aren't talking night and day here.
With very difficult to drive headphones certainly the effects realized by better amplification will be more obvious and substantial, but people need to be realistic, the P9 is a very easy to drive headphone. I have never had a headphone suddenly sound night and day better when switching amps, I'm not saying there aren't shifts, and some certainly are audible improvements, but repeating myself again, they have never been so significant as to really change the way the headphone's signature is perceived, more like minor differences. Again, I am not saying no difference is possible, nor am I implying minor differences can't be meaningful because they can.
Edit: a caveat/disclaimer, if the P9 had a very erratic frequency response that could also be a factor and in some cases yield more obvious improvements, but I as of yet haven't seen any real measurements so hard to say one way or the other.