You're going to have to drastically cut down the death rate for flu if deaths while there is a comorbidity (even if that comorbidity didn't result in death) don't count.
If you get attacked by a bear, go to the hospital, lose massive amounts of blood, and then end up dying of a heart attack because low blood level stresses out your heart, are you seriously not going to say that the bear was the proximal cause of death even if you actually died of a heart attack?