Does Congress have no input?
Of course they do. They could mandate such distribution, they could forbid it, or anything in between. Absent specific legislation, the disposition of surplus hardware is generally governed by the agency which "owns" the hardware. Bam-Bam can't, for example, legally shut down the CMP; it's a creature of Congress.
Congress has the sole authority in directing what the CIC can do. Congress can write laws telling Obama he must paint the equipment pink if they wanted. The President has a minor role in rules and regulations of the military.