Somebody, somewhere else, wrote an article showing how the PTS does in fact incorporate the Fleming short story. As for the rest of the story/film, the villain's lair is underground, we've got underground scenes at film's end. Both story and film take place in France. The story's got gypsies and the film has Grace Jones. Couple of other similarities too.
Both end with a fight on the Golden Gate bridge, and Fleming also quotes the Beach Boys.
Getting back to the original post, I wouldn't class TLD as the most faithful adaptation. One big difference is that in the original Trigger really is a KGB assassin, rather than an innocent dupe in an insanely convoluted plot hatched by the defector. The film makes Bond say he only kills professionals, which makes his refusal less shocking and less a dereliction of duty than it was in Fleming. And the film doesn't have the depressed, accidie-ridden mood of the story either--you don't get the sense of an increasingly bored and soul-sickened Bond waiting days to commit murder and slowly falling in love with a girl he sees on the street. That's not a knock on the film, which is still one of the best Bond movies. But it does mean that TLD is perhaps more true to the letter than to the spirit of the original. I'd place CR in that category as well. On the other hand, the films of GF and OHMSS noticeably deviate from their sources, but feel true to their spirit.