It has been reported, and it seems reasonable to me, that there are 50,000 deaths each year in the USA due to Influenza (Pneumonia). If this is the case then this follows by mathematics:
Influenza and Pneumonia are not the same. The former frequently leads to the latter in the case of bacteriological pneumonia. While influenza and some types of pneumonia are viral, they are different pathogens.
Your calculations don't take into account the "s" curve nature of infection rates as they peak over a broad population, and they assume that people can contract the same disease twice. After peaking, the infection rate will drop off due to the scarcity of previously uninfected victims among the population pool and the decreasing probability of these uninfected pool members contacting each other...