Dks01 Clearly, you have much more experience in this area than I ever could (or would want to have).
I only ever saw this once, and the funeral home in question did not have a funeral director handle that paperwork. Whether or not they were supposed to do that, it was someone in more of a sales position who handled the paperwork. Given the situation, I don't clearly remember if everything got a signature, but my recollection was that he entered the details into one of his systems (my impression was a Web-based system) and submitted it on-line; no paper, no signatures. The only things that definitely were on paper were the funeral home certificate and the invoice. We didn't see an actual funeral director until the day of the funeral, after the invoice was paid in full.
In Quebec, the certificate from the funeral home is beyond useless. One needs the declaration of death (from attending physician, etc.) to get the official certificate, and virtually nobody (banks, insurance) will deal with you at all until you have the official certificate issued by the Directeur de l'état civil du Québec.
Whether truly a clerical error at Service Canada or a funeral home, or something more sinister — given the apparent "request" that the woman in question said she never made, and the "neice" she doesn't know — something is definitely not right, and they need to take steps to address the situation, so that more people don't have to keep suffering through situations like these.