From the Official Code of Georgia, Annotated (Bold text for emphasis, mine)
16-11-39:
(a) A person commits the offense of disorderly conduct when such person commits any of the following:
(1) Acts in a violent or tumultuous manner toward another person whereby such person is placed in reasonable fear of the safety of such person´s life, limb, or health;
(2) Acts in a violent or tumultuous manner toward another person whereby the property of such person is placed in danger of being damaged or destroyed;
(3) Without provocation, uses to or of another person in such other person´s presence, opprobrious or abusive words which by their very utterance tend to incite to an immediate breach of the peace, that is to say, words which as a matter of common knowledge and under ordinary circumstances will, when used to or of another person in such other person´s presence, naturally tend to provoke violent resentment, that is, words commonly called 'fighting words'; or
(4) Without provocation, uses obscene and vulgar or profane language in the presence of or by telephone to a person under the age of 14 years which threatens an immediate breach of the peace.
(b) Any person who commits the offense of disorderly conduct shall be guilty of a misdemeanor.
(c) This Code section shall not be deemed or construed to affect or limit the powers of counties or municipal corporations to adopt ordinances or resolutions prohibiting disorderly conduct within their respective limits.
This does not specify the nature of the "fighting words" that would incite a breach of the peace - this merely states that uttering such words, of an opprobrius or abusive nature (target non-specific) would incite a breach of the peace. In other words, statements don't HAVE to be directed at a particular party - they could be directed towards a certain group or entity.
To illustrate: were this hypothetical individual enter into an establishment and state something to the effect of "God hates n*****s, and they will all burn," then that would UNDOUBTEDLY result in a breach of the peace - more than that, depending on where it's uttered.
As a law enforcement officer, I would have no remorse in charging the "victim" in this instance with disorderly conduct, under either the Georgia Code or the Savannah City ordinance for the same, and sending them to jail.
However, I would also be obliged to place the other individual under arrest for either simple battery, battery, or aggravated battery, depending on the nature of his injuries. Alternately, I could charge both parties with Affray, which amounts to fighting in a public place.
TL;DR: both parties are guilty of a crime, as established within the confines of a codified set of laws. No miscarriage of justice there.
With regards to holding the other subjects for questioning in an incident - not outside the confines of credibility to believe that they might have knowledge of an incident... but only if some others were questioned for a similar duration. Otherwise, there may have been more than a little stretching of police authority. HOWEVER: at no point were they under arrest, therefore there was no violation of their 4th Amendment rights.