That doesn't make any sense.
Yes, it is an anecdote. But that is all that is needed in this case. It speeds up combat in our game. It won't speed up combat in all games and it might not in yours, but it does in ours.
And I believe that you believe that it actually made your game faster. I am still skeptical, however. There may have been other factors that slowed things down before that were not present when the new rules were used. Or you might just not have noticed that it was taking longer because you and your players were more engaged with the new rules. Or any one of a dozen different things.
Now if your group was so engaged that you didn't notice it took longer, that would still be a good result. So there is that. But as for it actually being faster, I doubt we will get an impartial study under controlled conditions. So I am going to have to go with what my own mind is telling me based on the systems as presented and my own experiences. And those factors tell me there is no way Mearls' Grayhawk Initiative is faster.