The person who usually filled in the death certificate was the undertaker, with info that he obtains from a family member.
I don't know about the Dr part, I assume they usually fill in their part and sign it.
Alot of what is filled out on the death certs is info that comes from a family member and it may not be true info, the undertaker only goes by what he is given.
Perfect example- My great-grandfather was married 2x's. He had a daughter by 1st wife, when this daughter died many years later, the 2nd wife was listed as her mother when that totally is not true.
Many people do not understand how a death cert can be wrong, but it can be.
Hope this helps