CAMP FOSTER, Japan—On Thanksgiving Day, a 20-year-old American Marine stationed here on Japan’s southern island of Okinawa was playing parkour, an extreme sport in which participants jump over urban obstacles.

He fell from a wall onto the property of a public building as he back-flipped—and was arrested for trespassing and held for six days, before being released without charge.

To the Marines, it was an extreme case of overzealous enforcement for an innocent mistake. “We have no voice to say great injustice has been done to this kid,” said David Griesmer, a Marines spokesman in Okinawa.

To local officials, it …