The FAA will receive the results of SpaceX's investigation an issue a determination that they found the cause/reason for the anomaly, the steps SpaceX will make to address it, then the permit will move forward. This process can go back an forth several times (which it has in the past to Eloons chagrin) until the FAA is satisified and inspects the vehicle itself. That rocket was certified to fly by the FAA. By burdening the company to supply evidence that they have found the fault and have fixed the issue its a win win for both the licenser and the licensee. It's not perfect but the FAA treats everyone in this manner, not just SpaceX.
Note: I am in no way an Eloon fan, despise him, but I do have the utmost respect and enthusiasm for the 10's of thousands of young engineer's and employees of SpaceX. This is their Apollo program. NASA has 2 gigantic rockets with 50 year old engines that cost 40 billion dollars and is still using a 60's mentality in it's approach to space. The young generations need that inspiration just as we had with Apollo and the Shuttle. Plus if we have to have a Russian putting our people in Space it might as well be this fuck 
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