This really makes me wonder what kind of vet your "Dr. Dan" is supposed to be, as a real veterinarian that "keeps more than a hundred chickens himself" would know that this is not the case.
Nice try @CityFarmerRob and at least somewhat entertaining. ;)
Take a close look at your own pictures and you will notice that the broken egg (picture) has a different shell colour and texture than the one you are holding in your hand.
Someone is definitely pranking you hard. No need to spend on a vet visit or examination in more detail.
The egg might have already been there under the bedding when you put the cockerel in.
Candle the egg or put it in a glass full of water to see how fresh it really is.