My only experience of death certificates was when I registered my parents’ deaths, and my understanding is that this is usually done by a family member; presumably, in this case, their father. (Although I don’t think a final death certificate can be issued until an inquest has concluded.)
However, if their father did register the deaths and obtain the death certificates, I find it strange that he said he didn’t know what they did for work. When I registered my mum’s death, I stated “housewife” as she did not work, and for my dad I said “retired.” I was then asked what his occupation had been previously, and I was able to provide that information. I also registered my uncle’s death; as far as I knew he was unemployed, and that is how his occupation was recorded. I hadn’t seen him for a couple of years, but it didn’t occur to me to say I didn’t know, as I knew him well enough to think it was extremely unlikely anything had changed.
All of this is to say that the registrar or coroner will normally rely on information provided by the family, where there is one. In this case, there is. So I still find it odd that the father or family reportedly said they did not know what their children did for work.
It could also be as simple that the three young ladies were all estranged from their father and extended family and the family do not wish to say this publicly