I'm not so sure. I am unaware of any authority of the police to decide which individuals may step onto public property absent...
Yes, Georgia law does allow you to be in a public park with a firearm if you have a license. Being asked to leave or suffer arrest for criminal trespass only applies to private property, so I do not believe they can ask you to leave simply because you have a gun.
I think the guy is approaching this kind of like the Police pulling someone over for an inappropriate reason and then discovering drugs. I think it is referred to as “fruit of the poisonous tree” or something like that. In other words if they had not stopped this guy when he was doing nothing wrong there would have been no confrontation and no subsequent arrest.