I can believe that. Back in the 1990s I got the flu shot every fall. Due to a severe reaction in the late 90s I stopped getting the shot. I noticed that previously I would get lung infections 4 to 5 times a year, usually bronchitis. A few years after stopping the flu shots, I pretty much stopped getting lung infections. Now I only get pleurisy every few years and colds even less.
I stopped getting the flu shot and do not see any changes to my coming down with sinus issues.