I guess it is POSSIBLE that somebody would recognize the dog as a police dog, and that would harm future cases. It seems like a better idea simply to cut the footage of the dog in it, but I'm sure somebody on the COPS TV show had a good laugh at spending all day blurring the face of a dog.
What privacy does a chihuahua need? Why would a dog need his face blurred? They do not have the same rights and needs to privacy as a child. If a child's face doesn't get blurred when he is in a horrible situation (ex. his grandparents are overdosing in the front seat of the car), why would we, as adults, protect a dog's face before a child's? If we care more for the humanity of a dog than a child, there would be no hope for us.
No, it does not make sense to blur a chihuahua's face on television. There is no circumstance that I can think of that would justify protecting the identity of an animal, unless it's a parody on Funny or Die or part of a Beverly Hills Chihuahua sequel. I also think it mocks the practice of proctecting the identity of people who could be in danger if their faces were shown on TV.
No, it does not make sense to blur a chihuahua's face on TV because a dog does not need to be paid for appearing on TV. A dog also does not need its privacy protected. Therefore, only people should have their faces blurred unless they sign an agreement to appear.