"Sally - I believe they CAN claim for 'Arrangement' , but MUST Credit the composer of the melody !"

No - they can't do that.

They could register an arrangement and claim on it, but only with the permission of the copyright holder, who will almost certainly expect a percentage.

They may, however, use the tune without permission, as long as it is correctly credited to the copyright holder.

If they are claiming they wrote the tune themselves, but it is materially someone else's copyright, and that person chooses to take action, then they will loose the case (in a civil case - as with all copyright issues).

Tom