One of John F. Kennedy's Secret Service agents -- who was with him in the car that day -- says the famed magic bullet theory doesn't quite add up ... based on what he remembers.

Paul Landis shared his story with NYT, which will also be touched on in a new book of his due out in Oct. Here, he recounts what he says happened when the Prez was assassinated ... insisting the first bullet to hit JFK wasn't the same one to pierce Gov. Connally.

The reason that has been the official view of the U.S. Government for decades now is due to the findings of the Warren Commission -- which investigated the President's assassination, and concluded Lee Harvey Oswald was the lone shooter ... arriving to this conclusion, in part, because of this single bullet that was recovered in Dallas in the immediate aftermath.

Basically, Kennedy first got shot through the throat ... and almost instantly, Gov. Connally was also hit -- getting shot through his chest, wrist and thigh. Despite skeptics, for years, saying it was virtually impossible for that "magic bullet" to have caused so much damage the way it did ... Uncle Sam ultimately determined that's what happened, and closed the case.

They landed on the magic bullet theory because one of those sniper projectiles was found in the stretcher that was carrying Connally ... so they assumed it was the same one that had hit Kennedy to kick off the assassination. That's not how it went down, though ... per Landis.

He claims he actually recovered the first sniper bullet himself, which he says was lodged in the backseat behind where Kennedy sat. Landis says he snatched it because he thought it was a key piece of evidence, threw it on Kennedy's stretcher -- thinking docs would find it -- but presumes the bullet bounced off JFK's stretcher and into Connally's in all the ruckus.

In other words, Landis is now saying that the first bullet that struck Kennedy probably started and ended with him ... and did not travel on to hit Connally. That lends credence to the notion of a second shooter -- something conspiracy theorists have asserted for ages now.

The magic bullet theory has long been the subject of speculation/intrigue -- it was famously spoofed on 'Seinfeld' ... perfectly capturing how ludicrous the masses have found it.