The GBI took action on the only charge they had (it's not against the law to make a video).
No, Bryan was arrested because if Gregory and Travis McMichael committed murder (as they’re currently charged with doing), then anyone who assisted them in the murder is guilty as well. And since Gregory McMichael told police that Roddie Bryan helped them, Roddie Bryan has been arrested.
I don’t know how anyone would expect Bryan not to be arrested, given the charges pending against the McMichaels and the statements made by Gregory McMichael to police. If you have someone on trial for murder, how do you explain not arresting and charging the guy that one of the murderers says helped them do it? It’s obvious Bryan was set to be arrested.