“Is it a matter of public record when someone passes away, and are records such as Social Security public knowledge?”
A funeral home has to contact Social Security when they have a body.
They also report to banks, state income tax bureaus, etc.
When my husband died, I told the funeral director that I would notify SS the following as de died in a Sunday. He told me not to bother as, the minute that my husband drew his last breath, SS knew it.