"Veterinarians said it is possible for a newborn puppy's fur to be green because the placenta, which is green, rubs off at birth."
Humm, veterinarians or vegiterinarians? I've been there for birthin' many animal babies of many species but I have yet to see a green placenta. Sometimes the mucous plug comes out in a variety of colors including very intense green. But a green placenta would probably indicate a dead (long prior to parturition) placenta.
I don't know about the placenta, but the umbilical cord was bright green when he was delivered. I remember it vividly.
My son turned out fine, btw. He's joining the Marine Corps as an officer after he finishes his senior year at A&M.