Was I about to say this, lol. Any pad player worth a lick will be using their multiple parts of their thumbs (particularly the first joint of the thumb) in a rocking motion. This doesn't require them to lift their full finger off the pad. As Kimosabe points out, pads return to neutral by releasing the pressure of a direction. So the time between inputs can be incredibly miniscule. A stick has to travel back and forth which increases the time between inputs for the most part.
Also, because pads active by pressing down, you can actually shorten input time by holding close to the center and only applying pressure there to get the press. This is one of the reasons why an SPD on a pad is so damn easy, especially the non-shortcut ones.
Now, whether or not it's a clean input is another issue but pad inputs can be very fast, especially in regards to the d-pad.