The example assertions he was making were non falsifiable. However, if the claims were slightly tweaked to say something along the lines of:

"historically, a code modification like the one you've requested has taken 5n units of time. After refactoring, such a change will take n units of time."

You wouldn't perform an A/B test to prove your claim. The managers would simply have to trust you for the reputable engineer that you are, and hopefully observe substantially increased velocity after the refactoring.