As everyone engaged in aircraft manufacturing, testing and maintenance knows:
"The Job's Not Done Until the Paperwork's Done"
The Wright's documented everything. They did wind tunnel testing on their aerofoil designs - building their own wind tunnel to do so in the process. They kept their records for examination and did a professional job.
Other claimants may have flown before them, but in the event they failed in the follow-up - their design and development paperwork simply wasn't up to scratch.