I have seen such videos before. I have always thought it is the gentle handling that makes the naturally docile animals relax. Words do not matter.
I have checked with two of my veterinarian friends and they concur with the thought.
2:171 The likeness of such blind followers is that (of a herd of sheep) which hear the shepherd’s call, but hear in it nothing more than a sound and a shout. Deaf, dumb, blind, for they do not use their reason.
[This is subhuman level of existence 7:179. ‘Unq = Shepherd’s call. Shepherd here pertains to religious leaders who have learned some meaningless words or tenets, and a herd of sheep is the masses that blindly follow them. Kufr embraces blind following in addition to denying, opposing, or concealing the truth. Perceptual senses alone cannot distinguish human beings from the rest of the Animal Kingdom. It is the intellectual analysis that sets them apart]