I just can't seem to leave this one alone. I think because it seems to be a typical example of the complete loss of common sense in favor of definitions that appear to clarify but don't.
I am guessing that what your allergist means is that pine pollen doesn't usually cause the defined "allergic" reaction, that being an overreaction of the immune system. That would be why your kids would test negative, their immune systems are ignoring the pine pollen.
But it seems to me it is just plain old common sense that while all that "heavy" pollen is drifting downwards, some of it is going to be breathed in and end up in the respiratory system. The body is going to clear it out one way or another - if the immune system ignores it, that does not mean it isn't going to stimulate dripping, snorting and coughing as the respiratory system clears it out, same as would happen if it was dust or smoke that you were not "allergic" to, but that your lungs still didn't want in there mucking things up.
Your allergist can't see the forest for the tree pollen, imho.