Why would James go to GNR ? He knew Madison and Project Purity location long before, he didn't need to ask anything to three dog. No one has seen him in GNR building except three dog, no BOS soldier mention him.
He probably just went to Megaton to get some supplies and news of the wastelands and went directly to Rivet City from here.
He probably knows the wastelands very well, as we can see when he is coming back to Rivet City after the vault 112 episode. he runs and is hard to follow. He doesn't need a big head start.
Tjhen yes, Styles is right : Three dog is a liar.
edit : Perhaps Moriarty just advised James to go to GNR, just as he does with the player, but who really goes immediately to GNR (or at all ?). James didn't follow the advice and went directly to Rivet City.
So let me get this straight. Moriarty, for reasons best known to himself, tells the LW that James went to GNR, then Three Dog somehow hears all about James and Project Purity on the Wasteland graqevine, and finally, when James' child turns up at his studio, instead of saying "Yeah, I heard he went to Rivet City" decides to spin some BS story about having met him and how he's a "real stand up guy"? Why? It would be the height of stupidity to try to fool James'
child in this way. If he hasn't met him then Three Dog knows next to nothing about James, a fact which the LW could ascertain with a few simple questions.
"Could you describe the man you met to me?" "Could you tell me a bit about what he said to you?" It's a completely pointless and potentially very dangerous lie.
Look, this theory isn't actually
impossible, not quite, but it makes far more sense to accept that two independent witnesses who tell the same story are telling the truth than to believe some convoluted conspiracy theory that benefits neither party.
GNR building is surrounded by Supermutants for some time, how could james enter to meet Three dogs then ?
Lyons says something like "Super mutants have trapped our brothers at the GNR station, we are going to rescue them". No indication at all of
when this happened. Could have been days earlier, could have been hours. Perfectly possible that James got there and left before the mutants staged their raid.