As someone who has certified death many times, this is an interesting topic. There are two elements of the death certificate. The first is the direct cause of death, the second any significant conditions present which have had a bearing on the death.
As an example, one could certify the death as due to pneumonia, but in the second part chronic obstructive pulmonary disease. In the example of pneumonia you gave in the vlog, that would read in the first part Pneumonia, and in the second Advanced Parkinson’s Disease. Completing the second part is not compulsory.
In the case of your mother, with no other pathology present, Advanced Parkinson’s Disease is a valid cause of death, because if she didn’t have PD she would have died from something else.
Although it is not compulsory to complete Part 2 of the death certificate, that secondary cause is picked up in national statistics. That’s how stats are produced about alcohol related deaths. In the majority of deaths where Parkinson’s is present, it is a secondary factor.
As an aside, I once had a patient who died aged 106 who I had seen in good health a couple of weeks before. I discussed her with the coroner - you don’t get to 106 if you have a raft of chronic conditions. After that discussion, her death certificate simply read “Old age”. Unscientific, descriptive, but true.