Fully understanding the stress that the family are experiencing, as I had a very similar experience fighting for compensation for my mother when my father passed away as a consequence of asbestos related cancer (mesothilioma) about 6 years ago.
The family must start a paper trail. Write to the insurance and obtain from them the reason for refusal to make payment. When dealing with any matter that may have to be formally contested at a later date, then it must be in writing to avoid misunderstanding.
If the insurance company are disputing the cause of death then who issued the certificate becomes pertinent. There are many other factors that may be involved here, the competence of the Doctor may be in question, was the Coroner's Office informed if so will there be an inquest (will certainly delay payment), was an autopsy carried out if so has the report been published and do the family have a copy?
If there is an autopsy report does it contradict the cause of death on stated on the Certificate? Was the deceased on prescribed medication, have a long term illness or involved any incident that could have contributed to the passing. So many difficult questions it breaks my heart to point them out.
Sorry to appear a bit hard nosed about this, having dealt with the big battalions of the insurance world I have no respect for them or the people who make their decisions I just want the family to be best placed to get what is justifiable due to them.
<blood pressure now starting to fall.....and relax>