I don't know of any people who eat one thing all the time, and unfortunately cancer has claimed way too many of them. Realistically, this cannot be true, unless the one food the dog was eating contained carcinogenic chemicals. I don't know why people say things like that. Glad you asked instead of believing or repeating it for another. That is how some of the strange things get spread. One uninformed person makes a bizarre statement, another takes it as fact and then writes in online and we all know if it is online it must be true -- NOT!
But sometimes it is really difficult to disprove some of these crazy ideas once they catch hold online.