TL;DR: Yes, there's only shaky proof, and the Smithsonian isn't quite an angel when it comes to the presence or lack of truth in flight.
The Smithsonian had a rather shaky history with who flew first, even with the Wright brothers. They tried claiming the Bros didn't fly before
Langley, who was a Secretary of the Smithsonian (Whatever that is), whose plane actually was never proven to fly (Tests in 1914 to see if it
could were proven to include drastic changes from Langley's original design, thus irrelevant). His models worked, but the full scale ones didn't.
After the last Wright brother died, the folks giving the Wright brothers' plane, the
Flyer, to the Smithsonian did so under one condition: The Smithsonian could not claim that another person had flown before the Wright brothers, or they would have to return the plane.
So, naturally the Smithsonian wouldn't easily claim someone else had flown before them and risk losing the
Flyer. Granted, Whitehead didn't have a photograph of his flights, only a news article to back his claims up, and the Wright brothers certainly influenced modern flight a lot more than he did (Even if he
did fly before the Wright brothers, which will probably never be proven).
Still, all of the stuff flying around the whole deal is rather interesting.
(More reading, where I got most of this information, is
Here.)