evolution - Genetically speaking, are dogs exactly similar to humans and chimps both?

Richard Dawkins mentions in his book The Greatest Show on Earth that dogs are exactly similar to both humans and chimps. Supposing that a cell contains the genetic similarity between 2 species, he says

The human/dog cell should have an identical resemblance score to the chimpanzee/dog cell because humans and chimpanzees have exactly the same degree of relation to dogs. It should be identical, too, to the monkey/dog cell and the lemur/dog cell. This is because humans, chimpanzees, monkeys and lemurs are all connected to the dog via their common ancestor, an early primate (which probably looked a bit like a lemur)

He later says that this will be found within "statistical margins of error".

Because the common ancestor of both chimps and humans was more similar to chimps than to humans, it stands to reason that chimps will be more genetically similar to the common ancestor than humans. Therefore (not a direct therefore), dogs and humans can't be exactly similar as dogs and chimpanzees are, even theoretically. Humans and apes are even more dissimilar. Therefore ape/dog cell will not be exactly same value as the human/dog cell.

Please explain where I am wrong.