Most deaths occurred before the vaccine was available.
Most serious illnesses will compromise the immune system. A compromised immune system will make you more vulnerable to any infection. So the most common and most spread infection will then also naturally be the most common one to trigger death.
If someone has aids, which is a decease that compromises the immune system, and then dies from pneumonia. Did they die from pneumonia or aids?
The statistics are a total mess in my opinion and any being professed with any exactitude should be taken with a grain of salt.