Second is the local PR for your group. How much PR do you get in your local paper? You think you might get more if this trip is linked to a nomination by the mayor? You think it will be easy to get recognition for your program by the city with the link to the mayor? You plan on asking the city for help or permission for anything in the near future? You think getting a picture in the paper or on TV of your drum major and the mayor 'accepting' this 'prestigious invitation' wouldn't be good PR?
Does the trip firm want to sell you a DC trip? Sure - that is kinda why they exist. Is it 'ploy'? Yes, but I wouldn't make it sound nefarious. Think of it more as a business model. And again, it is the DC parade on July 4th. Not like they are trying to sell you on being the Texas rep in a July 4th parade in East Montgomery AL.