Not at all. Here is the quote I called Horse Puckey on.
"The weak hand needs to be an integral part of the two handed grip. For me that is where most of the recoil control happens. Trigger control occurs with my strong hand. Most shooters try to do too much with their strong side of their body. This is a natural thing that we need to overcome for really fast shooting. Fast shooting doesn’t happen when the strong side is tensed up. This is when you will see shooters have trigger freezes, and horrible follow up shots. "
Burkett says that a strong weak hand grip allows faster manipulation of the trigger finger, and says that when the strong side is tensed up, you will see trigger freezes. My point is that if one can shoot as quickly one handed as two, (as Caleb states) then it isn't a product of the weak hand at all, since there is no weak hand on the gun.
And, as Caleb also pointed out, one will not be as accurate, but that is not the issue here.
While I'm admittedly one of the least experienced pistol shooters on the forum, I think the issue is entirely being able to shoot as fast as possible accurately.
Personally, I really think having to specify that you can shoot "as fast" with one hand if you entirely disregard hitting the target is getting a bit pedantic.
Just my $0.02 worth.
I agree with this statement 100% - I can shoot much faster accurately with two hands on the gun, and relaxing my strong hand also helps eliminate trigger stutter. Here's the example I use in classes:
Make a fist as tight as you can with all your fingers except your index (trigger) finger. Now try and wiggle your index finger as fast as you can without relaxing your hand. Now relax your hand and wiggle your index finger. It moves faster with your hand relaxed than it does with it all tensed up.