Crew members also said that Osbon had "showed up at JFK later than he should have for the flight and missed the crew briefing."
The FAA called the incident a medical emergency, but law enforcement sources have called the outburst a panic attack.
"As of now, he's been taken off all active duties and responsibilities pending further investigation," JetBlue spokeswoman Tamara Young said.
An unruly Osbon was subdued by at least five passengers after his co-pilot reportedly locked him out of the cockpit when he displayed potentially dangerous behavior. The flight from Kennedy Airport in New York was diverted to Amarillo, Texas.
On the ground, Osbon was taken off the plane in handcuffs and a wheelchair by Amarillo police. He is now in FBI custody.
Osbon's last medical exam was in December 2011, according to the Federal Aviation Administration. His FAA record has no accidents or incidents and no enforcements.
Family and friends say they are shocked to learn of the incident. Bud Lawyer, Osbon's next-door neighbor in the small Georgia community where he resides with his wife, told the Associated Press that he knows Osbon does attend church but rarely spoke of it, and the two would only casually talk about events in the Middle East.
"He wouldn't intentionally hurt anyone," Lawyer said. "He's a kind-hearted, generous, loving teddy bear. It's totally out of character for this to happen to him."
ABC News' Kevin Dolak, Christina Ng and Josh Haskell contributed to this report.