This is definitely true, although I'm not sure what she was talking about with one specific breeds of dog. Many, many dog breeds with long hair are double coated, meaning they have a layer of soft, fluffy undercoat and a layer of coarser guard hairs which act to protect the coat. In the summer, much of the undercoat is shed out (and often must be combed out, especially in a dog with a thick undercoat), allowing the dog to stay cooler without this insulating under layer. The guard hairs also provide a layer of protection against the sun and insects. If you shave the coat of these dogs, the body's hair production system kicks into overdrive, sensing the lack of protective guard hairs, and begins to make massive quantities of undercoat to try to compensate. To make matters worse, as the new guard hairs come in they become entagled with the mass of undercoat, often leading to a dog that is a matted mess, and is even hotter than it was before you shaved it. The proper approach to handling a double coat is to "strip" it when the dog is wet, using a fine toothed comb to remove the loose undercoat. Products like the furminator work for this task also, but may damage the coat or skin if overused.
(My mom is a professional groomer specializing in large and giant breeds, so this is a topic I have heard a lot about!)
but the energy change due to evaporation (a change of state) is more significant than the energy change in just warming up more water. Unless it's humid, the sweat will evaporate anyway so I don't really buy into it...
