> More people complain about having it, but they don't need to go to the hospital over it.

It seems that even the number of reports to the CDC (without hospitalization) has been decreasing after the peak of Jan. See https://www.cdc.gov/flu/weekly/index.htm

> They want you to get vaccinated more than they want to show you an accurate model of how the flu spreads

Agreed, but you'd think there are arguments and facts that don't need to be twisted to make their point. Bending the truth can accomplish the opposite of what they intended to do.

A common reaction to this kind of method is "if they're going to exaggerate and lie about this, what else are they lying about when it comes to flu vaccination?" - it destroys credibility quite quickly and fuels conspiracy theories.