Back then, it was obvious that Covid caused the death or at least contributed mostly to the death, especially in vulnerable populations.

For instance, if you compare two groups of elderly individuals with similar baseline characteristics but one group got Covid. It's pretty clear that the Covid group had higher risks of death - this much is clear from basic research. But if one group got the vaccine instead, the risk is no longer apparent and the risk of death might even drop in the context of high covid transmission.

In animal settings, it's also clear that Covid causes a myriad of health problems. Give mice covid and the effects are clear. But when it comes to vaccines, such effects are absent. Vaccinate mice and we almost never see an adverse reaction.

Therefore, it's obvious that covid kills (esp in vulnerable population) but not so obvious when it comes to the vaccine. That's why determining the vaccine as the cause of death requires much more thorough investigations than covid.