I'm not trying to be a dick about it, I'm just pointing out that there isn't a single bit of medical or scientific evidence that backs what you're claiming. Mainly because it's a medical impossibility, since the two are are completely different viruses. It's like trying to cure a migraine by applying anti-fungal cream to your toes.
The virus that causes most viral pneumonia is the Rhinovirus, which causes most colds as well. Yet they offer a vaccine for viral pneumonia. If what you say was true, would they not just give the flu shot? Do you get both vaccines? If so, why? I mean, you claim the flu shot works on both.
As far as insulting your doctors, I did no such thing. I think you either may have misunderstood something they said (not saying you did), or you are in a unique situation where they take the "every little bit helps" approach, just like my father is in. Maybe they recommend it for you because they want you to have all the help you can get, which is understandable. But not getting the flu vaccine will absolutely not make the average person any less likely to catch a cold than getting the vaccine will prevent one. It isn't a cold vaccine, there is no such thing. And if what you are saying was accurate, it would be incessantly hyped all winter long as a reason for people to get the flu vaccine.
And I wish you would say more in medical threads, even if it's just a guess, because doctors always miss things, and all the input you can get helps. I have an issue going on currently with no explanation that's driving me bonkers, and I'd love if something as random as a message board post would lead me and my doctors down the right path.