It's the opposite. The absolute occurence of stroke was higher in people who got the vaccine, but other risk factors were also higher; adjusting for those, they

It's the opposite. The absolute occurence of stroke was higher in people who got the vaccine, but other risk factors were also higher; adjusting for those, they found a "less-higher than expected" amount of stroke, which they attribute to the flu vaccine. If you have a lot of faith in these sorts of statistical adjustments and the assumptions behind them, then you may find this result compelling.