Here's my take on it. I think the statement "bands make you slower" is fundamentally wrong, except, perhaps, on the very surface.
Take the Enamait punching drills with bands. You are slowing down, but you are still, neurologically, punching as hard and as fast as you can. This is going to stimulate the Type II muscle fibers (a's, b's, x's, or whatever) because of the nature of the signals the nervous system is sending. So, you are moving slower, right, but the nervous system is telling your brain and your body that you are moving as fast as you can.
Bands, when used properly, allow you to match resistance to the strength curve of the movement. So, if you are squatting 135 with the barbell, you have 135 at the bottom of the movement, which feels heavier, due to leverage, and 135 at the top of the movement.
When squatting fast with this weight, if you don't decelerate yourself at the top, you are going to jump off the floor. In many cases, this isn't very desirable, unless you are doing it for a reason.
If you are squatting 135, and using bands to that add 60# of resistance at the top, then you are still getting the 135# squat in the bottom (providing the band deloads correctly) and then you are getting a 195# lock out, and the resistance gets harder the more leverage you have. You don't need to decelerate as hard (if at all) so you can keep pushing harder and harder until the lift is finished.
In addition to that, the enhanced eccentric allows for a more powerful concentric, and this tends to be faster.
Louie Simmons, from the Westside Barbell Club, used a Tendo Unit to measure the speed of his lifters speed benches. He found that in every case, adding bands to the speed bench, enhancing the eccentric, made the concentric faster and more powerful with a similar overall load. I believe that someone in John Davies' Renegade Training organization also performed similar experiments with the Micro Muscle Lab.
The whole "bands make you slower" thing is just a wrongminded concept. Dan Wagman of "Pure Power" subscribes to this theory and seems to sometimes make it some kind of crusade to promote this idea, but the anecdotal evidence completely overwhelms the theory.
Bands will slow down the exercise, but they don't make you slower.