From my understaing, not quite.
From the same link that Sunshine provided:
"The Supreme Court reversed Street's conviction because his comments, considered a possible factor in his conviction, were constitutionally protected by the First Amendment. Emphasizing that the mere offensiveness of words does not strip them of constitutional protection, the Court again noted that fighting words must present an actual threat of immediate violence, not merely offensive content."
The fighting words doctrine does not protect whatever words are spoken. Only offensive speech. If a person conveys a thread of immediate violence, that is not protected under fighting words.
ETA: Just to be clear I'm not saying there is any evidence of fighting words that night.
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