I can't find any case law which directly answers your question; as far as I am aware, no case has ever been prosecuted under that law for the type of scenario we are talking about (but just because it hasn't happened yet, isn't in itself a bar for it happening some day in the future). This law never says the false accusation has to be made to a law enforcement agency, even though similar laws in other jurisdictions do explicitly say that; I don't see why a court would insert that requirement when the text doesn't explicitly contain it. But of course, nobody can be certain unless some day the matter actually comes before a court to decide.