Disclaimer: I am not a medical doctor and this is not medical advice. My goal is to empower you with information. I will not take a position on whether you should or should not get vaccinated. Please make this decision yourself, consulting sources you trust, including a caring health care professional.
"This should always be assumed about every paper that leaves out the underlying, unadjusted data, on any topic."
This is a salient bias--data hiding bias.
There is also comparator bias--perhaps flu jabs increase mortality more than no flu jabs in the general population.
And healthy vaccinee bias, of course.
See Norman Fenton St Mary UK work on those data .. he explains the higher initial mortality in the unvaccinated as mis classification.. by adjusting it shows that there is higher initial all cause mortality in the vaccinated..