The San Antonio Express-News reports an affidavit says William Ware told police he was drunk, a "genius" and on an FBI training mission.
The FBI says the 22-year-old San Antonio-area man isn't with the agency.
Bexar County jail records show Ware was being held Thursday on charges of driving while intoxicated, criminal mischief, possession of a prohibited knife and criminal trespass.
Online jail records don't list an attorney for Ware, who was arrested around 3 a.m. Wednesday after police received a report of a motorist seen driving through a taxiway and on a runway.
An airport spokeswoman declined comment.
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