DNA tests can absolutely be done to identify individual dogs. We had our dog's DNA tested to see what breed(s) he is. But, more specific tests can be done. The Arabian Horse Registry began requiring hair root DNA testing in 2002 instead of blood tests for parentage verification.
Yorkies don't shed like some breeds. Their hair grows and needs to be cut. But, like people, they do lose hairs. I betcha there were Yorkie hairs in the Anthony vacuum cleaners.
It would be damaging to Casey if Yorkie hair was found on the duct tape.