I'm speculating on joint U.S. Navy / NATO exercises as the reason why the U.S. Navy has never identified all of the ships that were in the area that night. Just a possibility.
There's no reason why the U.S. Navy could not have been responsible for it themselves -- it's not as if that kind of thing hasn't happened before (the Iranian airliner shot down back in the early 1990s).
If it was shot down by the Navy, every sailor on that ship would know. Secrets like that don't keep.