J, I fear it is not quite that simple. You cannot call something a parody
unless it is. Just labeling something aparody does not absolve you of
copyright issues. It must be truly a parody. This is easy to do, so you
are correct that a parody is not a copyright violation, but we cannot let
people think that just calling something a parody when it is not is legal,
it is not.
In a nation where children are sued by the RIAA for anything even resembling a copyright violation, we must unfortunately, be careful. We need not be paranoid, but awareness of the law is important.