Posting you support veterans but actually not, is that false advertisement?

There is a restaurant here that says it supports veterans by the sign it has posted by their entrance. There was a camp of homeless veterans on private land about 100 years from the restaurant and hidden much by the trees. The vets did not bother the restaurant or its patrons, yet the restaurant owners has campaigned and complained to the city to the point the city is pressuring the owner (who knew they were there, but did not care because they were not bothering anyone) to toss the vets off. To post a sign saying you support vets as a way to boost business, but wanting to push out homeless vets causing no harm, is that akin to false advertisement or posting a sign under false pretense?