These researchers noted that vaccination rates for the flu among high-risk senior adults rose from a low 15-20% prior to 1980 to over 65% beginning in 2001. However, counterintuitively flu-related mortality rose dramatically.
The researchers performed their calculations and concluded the flu-related mortality rate was very close to what would have occurred had no vaccine been available!
In fact, there were so few flu-related deaths some years (the American Lung Association reports flu deaths as low as 257 in 2001, 727 in 2002, and 411 in 2007. This is in stark contrast to the Centers for Disease Control that says there are ~36,000 estimated flu deaths annually.
The US news media in concert with the Centers for Disease Control continue to issue scary reports of ~14,000 to 36,000 annual deaths from the flu.