Long-Term Care Insurance Partnership Program Act of 2004 - Amends title XIX (Medicaid) of the Social Security Act to: (1) change from mandatory to discretionary a State's authority to adjust or recover medical assistance correctly paid on behalf of an individual who has received (or is entitled to receive) benefits under a long-term care insurance policy; and (2) repeal the grandfather date for cases to which such adjustment or recovery authority shall not apply. (Thus applies such exception to all State plans meeting specified requirements, and permits additional States to enter into long-term care partnerships to promote the use of long-term care insurance.)