Outdoor cats definately need to be vaccinated against it. Even the vaccination doesn't 100% guarantee they won't catch it, but it helps their chances. Being spayed or neutered has nothing to do with it, other than the fact that unfixed cats fight and mate more, thus creating more contact to possibly infected cats.

I've also not found it to be true that they stay away from sick cats.

My cats are strictly indoors, but I do foster a lot so mine are vaccinated yearly to be on the safe side.