His story about being a Navy SEAL wasn’t so fishy after all.

The Virginia man arrested for gun possession in Manhattan Thursday and thrown in a psych ward when he claimed to be a member of the elite military unit but couldn’t provide proof was telling the truth, The Post has learned.

Shaun Day, 29, was on a two-week leave when cops harpooned him for running a red light at 12:30 a.m. at Second Avenue and East 26th Street.

When cops searched his pickup truck, they discovered a 9mm semiautomatic and three ammunition clips.

During the arrest, Day was rambling incoherently and harped that he was a SEAL — but had no proof for cops.

He claimed he was an elite commando with “top- secret clearance,” cops said.

Sources told The Post the Navy sent staffers to talk to Day in Bellevue Hospital, where he was undergoing a psychiatric evaluation.

“He was released [Friday] in their care, and they were going to treat him for post-traumatic stress,” a source said.

The charges against Day of weapons possession and a traffic violation have been deferred.

SEALs, the Navy’s Sea, Air and Land teams, are credited with killing Osama bin Laden in Pakistan in May.