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The law says publicly means at a place open to the public or at any place where a substantial number of persons outside of a normal circle of a family and its social acquaintances is gathered.[1]
More radio use infringes than you think. But performing rights organizations can't force their way into work areas not open to the public. Infringement by individuals tends to be transient and anonymous. Suing individuals could provoke a backlash. And courts would be more sympathetic to individuals claiming fair use.
My claim is consistent with the statute. Yours isn't. It's up to you to find case law.