The scene in Los Angeles was caught on video by police body cameras.
At least two others were injured.
The vice president's plane had only been in the air for 30 minutes when the issue occurred.
Britain's Birmingham airport had heavy crosswinds due to Storm Ciara.
The agency says these plastic items could be mistaken for an explosive device.
A witness said the small plane's abrupt landing was the most amazing thing he'd seen in a long time.
Ten passengers were taken to a hospital.
The preliminary report recommends that the flight control system should be reviewed by Boeing.
Boeing says its safety review met "all certification and regulatory requirements" set by the FAA.
Some passengers said they were praying while others laughed off the aborted landing attempt.