Unfortunately they lost me in the opener with this:
There is no difference genetically between an old pure-bred dog with hip arthritis and an old mixed breed dog with hip arthritis. They both have hip dysplasia. The pure-bred dog may have received the label many years earlier due to early age screening, but the disease process is the same.
Hip arthritis is hip arthritis. Hip dysplasia is hip dysplasia. They may occur together, and hip dysplasia certainly usually leads to arthritis, but dogs without hip dysplasia can certainly develop arthritis in their hips as they age as well. Sigh.