Are neighbors' ants our fault ?

Our neighbors next door have had their house for sale for six years! This is their second note to us. The first had to do with our needing to get our yard mowed “since we are trying to sell our house.” Today’s note said they have “carpenter ants and Terminix “traced” the ants to YOUR house.” So happens we have an automatic insect misting system along the entire perimeter of the house including on top of the fence. Could the ants be racing over to their house to escape the chemicals?
Oh, I wish we could move to the country.