An HOA is not a Court of law. An HOA is an administrative body. The right to face one's accuser is a right in Court, not the HOA. So this does not translate into an HOA right, unless it is written into the bylaws, covenants, or declarations of the HOA.
If you wish to know who filed a false complaint but the HOA is not cooperating, you could technically sue "John Doe" for defamation and file a SUBPOENA against the HOA. This way, the HOA would have to provide the name. Once the name is ***** ***** suit would be amended to change the name of the Defendant from John Doe to (proper name) and the suit would continue.
Whether or not it is worth going though all this trouble - this is your decision, of course.
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