Putting it on the blockchain ensures you can always go back and say "see, at this date/time, this key verified this file/hash".. If you know the key of the uploader (the white house), you can verify it was signed by that key. Guatemala used a similar scheme to verify votes in elections using Bitcoin. Could the precinct lie and put in the wrong vote count? Of course! But what it prevented was somebody saying "well actually the precinct reported a different number" since anybody could verify that on chain they didn't. It also prevented the precinct themselves from changing the number in the future if they were put under some kind of pressure.