My father apparently died of pneumonia. Not the cancer that had just about reached every part of his body. I found that very strange.
Whilst I don't know what happened to your father, I can envisage that it would be possible for someone with late stage cancer, which would have killed them shortly, to be killed by something else first.
To give a vivid analogy...
I could be crossing a road, start to have a heart attack, collapse and be run over and killed by a lorry crushing my head and chest. It may be that the heart attack was such that if the lorry hadn't killed me, the heart attack would have done so maybe a few hours later, maybe even just minutes later, but it would still be the lorry that killed me.
I suppose you could argue that it was having the heart attack that caused me to fall and that if I hadn't fallen, I wouldn't have been run over, therefore it was the heart attack that killed me, but that would be the sort of causation people think of in terms of negligence actions rather than immediate cause of death.
This is why I'd never be able to fill in death certificates. It would fry my brain as much as benefits forms.
Benefits form analogy...
I remember a question about preparing food. Ah, but what was the problem? The attentional memory problems that are a feature of some sorts of bipolar? The alternating paralytic inactivity of some phases of bipolar and the dash round trying to get everything done of other phases? The tremor from my ataxia? The failure to judge distances between knife and food or whatever because of my vision? Etc., etc.
I think causes of death on forms could be much better shown, but only by re-designing the forms. (I've never examined one closely, only seen quick glimpses of them on videos.) Even then they'll still be problematic and I think that often professional opinion rather than absolute certitude will always be a significant factor.