The guy, who called himself Greg, got interviewed by the BBC Saturday in Butler, PA right after everything went south -- just outside the rally itself -- where he says he and his friends were partying, only to head up a hill outside the facility to watch Trump's remarks from afar.

That's when Greg says he and his pals saw a man shimmy up a nearby building -- which was also outside the main grounds of the rally -- with what he says was a rifle in hand.

Of course, the alarm bells went off ... and Greg says he and his group started to scream and yell for help -- with Greg claiming he even flagged what he was seeing to nearby police officers ... and he even claims he got the attention of the Secret Service, who was monitoring from across the way. Greg says he saw agents watching him/the gunman with binoculars.

Unfortunately, Greg says his warnings went unheeded -- at least at first -- and before he knew it ... 5 shots rang out from the roof, only for law enforcement to swoop in and blow the shooter's head off ... Greg's words, BTW. He's dismayed they took so long to respond.

It's an incredible recounting ... and if it's believed to be true as described, it's concerning.

FWIW, there's a video going around that purports to capture the body of the alleged gunman on the roof after he was neutralized. We have NOT confirmed this as authentic, but it does appear to show a body lying limp ... with folks on the ground looking on/commenting.

As we reported ... Trump appears to have been nicked in the ear as shots rang out. He's since been taken to a hospital and is in stable condition. In the immediate aftermath of the shooting, he was bleeding from his ear.

Trump also pumped his fist in defiance as he was escorted away by Secret Service. Reports say that at least one other rally attendee was tragically killed during the whole ordeal.