This claim is false.
Dogs wagging their tails is a way of communicating a variety of complex emotions. It depends heavily on the direction as well as speed of the tail wagging to hint at what a dog is trying to communicate. According to the American Kennel Club, a trusted organization for training, breed, health, and the overall information of dogs, mentions how, “In some ways, tail wagging serves the same communication functions as a human smile, a polite greeting, or a nod of recognition,” which was specifically said by Dr. Stanley Coren. A dog's tail wagging indicating that they are friendly may have some truth to it in some instances; however, it is not entirely correct for what was mentioned above. The American Kennel Club later gives an example in the same article, "Why Do Dogs Wag Their Tales" where it says that, "A slow wag could mean that a dog is unsure and feeling insecure about a situation." Here is the website for this information:
Another website that focuses on dogs mentions information that is very similar to the source above. The article, "Why Do Dogs Wag Their Tails?" from The Healthy Pet Club mentions how "[d]ogs will wag their tail to convey a range of emotions: happiness, nervousness, feeling threatened, anxiety, submission and excitement." Here is the link for that:
Both articles above share an expertise on dogs, so they are most likely valid and reliable. To make sure that the information these articles are sharing is true, I looked up Dr. Stanley Coren who was mentioned in the first article presented. He is a psychology professor from the University of Pennsylvania who studies dogs. He has his own website where he demonstrates his knowledge and expertise on dogs. There, he touches on the topic of dogs and their tail wagging. He mentions how, "[s]ome tail wags have totally different meanings." On his website he goes more into detail about the different meanings. Here is the website: