Photographic evidence. There is a photo of the SS with a M-14 clearly out in the trailing car as it comes out of the triple overpass. At the 6th Floor Museum. Sorry.
Again, I don't see someone making this sort of mistake by announcing a particular man shot Kennedy with a particular gun. The idea that he didn't even get the gun correctly identified seems implausible to me.
So perhaps you have a photograph of one of the Secret Service agents carrying an M-14, but unless it is Hickey, it doesn't quite disprove the man's claim.
Perhaps it is unlikely that one Secret Service agent would carry one thing, and another would carry a different thing, but I have no knowledge on what they would or would not have done in 1963.
On the other hand, if you are correct about this, the whole story is a ball of crap.