If the originality of the crossword has no value, why would it matter whether someone's claim that it is original is true or false? The most logical basis for attributing value to the claim of originality is that there is value in the originality that bleeds through to the claim.
Compare e.g. someone being jailed for resisting arrest when there was no justification for arresting him in the first place.
The law tends to disagree: crossword puzzles are copyrightable material just like any other published text is, so their value comes from the material that they help sell, whether that's a newspaper, or a crossword puzzle book, or a website, or any other published, in the legal sense, work.
But misattribution is not a problem at all in that analysis. It's just as illegal to violate a copyright with proper attribution as it is if I claim the work is my own.
The law doesn't care whether you claim a copyrighted work is yours or not. It cares whether, if you copy a copyrighted work, you have the license to do so.
Compare e.g. someone being jailed for resisting arrest when there was no justification for arresting him in the first place.