I wouldn't trust some local government flunky on this, I would ask for (or find for myself) the zoning and property tax standards that apply. Temporary structures-- often defined as those without a permanent foundation, such as a pole barn-- are not taxed or are taxed at a very low rate in some jurisdictions.
I'd check it out for myself... sometimes these folks don't really know the specifics of the law, but people just don't think to question them.
Heck, put the coop on wheels and move it around so the chickens can graze and fertilize different areas. Let's see them call that an "additional structure." :laughing:
Just my $0.02.