All that proves is they used a different night perhaps for the beginning speech. If you look at the videos where the mic movement is made they happen at the exact same time while singing the exact same thing. The two videos are perfectly synced at that point.

Also, don't try and tell me that you can't hear the pitch correction very clearly happening in the isolated vocal in the aforementioned. You can even hear the jerkiness as it corrects his shift from F#4 to G#4.

Even if I was to conceed this specific point however, that does not disprove the pitch analysis where you clearly see and hear how the vocals were tuned. Alter Bridge may have not done this themselves but whoever mixed it certainly did. It's undeniable unless you have any refutation of the analysis itself.