Taking the video at face value I don't think his yelling slowed things down that much, he was just showing it registered and the drives had to compensate?
I can make a few guesses, but I'm honestly not sure enough to take the video at face value.
15,000RPM is extremely fast for platters to be spinning, anything can disrupt reads/writes to them. Server drives must be built to take into account drive vibration from nearby drives during disk activity.
I mean, you have probably heard that the entire reason 15,000RPM is the limit is because any faster and the physical platter would begin to fracture and then shatter violently... the outer edge of the platter would already have to be vibrating to some extent and even more so if it is sitting in a rack with ~19 other drive platters spinning at 15K RPM... And you've probably taken apart drives before, those platters seem like the most solid, rigid discs imaginable and they don't flex an iota.