1:15 PM PT -- A rep for Secret Service tells TMZ ... "The Secret Service cannot provide the details on our means and methods of protection, but we can confirm that at no time were any Secret Service protectees in the vehicle while the individual was walking down the alleyway. These claims are inaccurate. The photo in question was upon departure and not during the alleged incident."

However, TMZ has spoken with an eyewitness who tells us the armed security guard approached the window and observed Obama inside using a laptop ... and because the guard was armed, he quickly moved away from the SUV.

Barack Obama coming inches away from an armed stranger in a Hollywood alleyway is the latest stunning lapse of Secret Service security -- an absolutely shocking scene that played out last weekend ... TMZ has learned.

The former president was sitting in the back seat of his SUV Saturday around 7:30 PM outside hot spot restaurant Mother Wolf -- and that's when the armed man approached the vehicle, in his capacity as a security guard for a bar mitzvah going on upstairs from the restaurant.

We spoke to the armed guard -- who asked us not to use his name -- and he says he went downstairs to check the scene, because someone told him it appeared federal agents were outside, and they didn't know why.

He says he walked out in the alleyway from a staircase, looked to his right and saw 2 men -- who turned out to be Secret Service agents -- then looked to his left and saw a black SUV with Dept. of Homeland Security plates.

He snapped a photo, assuming it was some dignitary, but had no clue it was Obama until he got closer to the passenger side, and looked into the backseat to find see the former prez using a laptop.

The guard says he panicked, realizing he was armed and could be taken out by Secret Service at any moment. So, he quickly walked away from the SUV, and out to the street where he said hello to the agents. He describes them as being startled to see him.

He turned around, walked past Obama's SUV again, and walked back upstairs to the bar mitzvah. Then, about 30 minutes later, he says his boss asked him to hand over his credentials and his license to carry a concealed weapon for the Secret Service.

Everything checked out, and everyone went back to their jobs at hand. Barack's daughters Malia and Sasha joined him later for dinner at Mother Wolf -- but, the security guard says what happened was "definitely a security lapse on their part that there was no one on the backside of SUV, nor covering the stairwell" ... which he used to approach the SUV.

He adds, he easily could have tried to open the door had he been someone trying to harm Obama. As for the agents' actions that night, he says, "I think they were obviously embarrassed by the situation."

Obviously, this comes on the heels of the Secret Service coming under heavy scrutiny for 2 attempts on former president Donald Trump's life within a few months.

We've reached out to the Secret Service about the Obama incident, but no word back yet. Coincidentally, a Senate committee issued its final report today on the agency's failures in protecting Trump -- and now it could have more explaining to do.