For your patients sake I hope you wear a mask throughout flu season. My sister's a nurse and they just recently had a small outbreak at her hospital both patients and faculty suffered. It started with a coworker on her floor (that wasn't vaccinated).
What science is there to it? A marker is created an identifying antibody is made and the body moves on until called into action if need be.
I do agree that fresh air and activity gets the body going helps strengthen immunity and absolutely helps in quicker recovery.
I also went years without a flu shot and then years with getting a flu shot after being around others kids and of course for the health of my own i felt it necassary. No flu since I was a teen. And I get handed hundreds of scripts and in contact with dozens upon dozens of people with flu and flu like symptoms regularly throughout the year. If it doesn't help... it sure doesn't hurt to get one either.