The mode of transmission of Mad Cow Disease, also known as Bovine Spongiform Encephalopathy, starts from a diseased cow. Any meal which contained bones or diseased cattle organs carried the risk of passing on the disease. If the cattle feed was contaminated, healthy cattle can become infected.
Assuming that there was some kind of dog food that could cause similar problems, a similar transmission pathway would be through a sick dog. A previously healthy dog would've become sick, or at least a specific organ system of the dog. Thus, people assume that the dog ate contaminated food.
In developed western countries, the transmission route had come to a stop at this point.
But in some other countries, the route of transmission has not stopped here.
Most Chinese people didn't eat dog meat, but there were a few people who enjoyed it.