It's one of them usual time travel choices: does the travel technique in this particular adventure fall within category A or B? That is, is time a single path which can be rewritten if one knows how to go back to a certain point? Or does interference with a certain point create a divergent timeline?
Both types of adventure should be possible. Even if the world is built so that time always branches out, certain time travel techniques should ensure that our heroes always return to the one particular future branch that was created due to their past interference, and thus supposedly to one that was remade to their liking. Other techniques wouldn't do this.
If we assume that time using slingshot travel is a single rewritable line, then what our heroes did should work all right as far as most of the universe is concerned. What this approach shouldn't explain is what happened to the original Enterprise - the one that tore apart Christopher's plane and got recorded on USAF files as a UFO. Why wasn't she present when Kirk traveled back in time? We can always assume that she was, and that the second ship nicely but firmly bumped her aside at a crucial moment (supposedly when she was sensor-blind), causing her not to destroy the F-104. USAF records should then remain unsabotaged, but they would only record the two radar blips of the two starships, not any close observations by Christopher who was dazzled by the transporter glitter and didn't see a thing.
Or then Christopher was blinded at such a moment that he lost track of the ship and ceased to be seen as a threat by the "first-pass" starship, so no tractor was applied.
If time branched out, then Kirk could have hit a slightly different branch the second time around, avoiding his earlier self. But those adventure types are usually unsatisfactory, because it sounds hollow to "mend" one time branch and feel good about it when another remains unmended...
In any case, it makes sense for Kirk to go back in time and put some things right, such as prevent his former self from destroying Christopher's plane. It makes no obvious sense to beam the "first-pass" Christopher and Sarge to the bodies of the "second-pass" Christopher and Sarge, though - except perhaps as a legal formality. "We didn't really kill them, we just cremated them within their own bodies" or something like that. In the end, the "first-pass" two would still be dead, their lives and thought processes permanently discontinued. Which was probably the humane thing to do, if both Kirk and McCoy for a rare once could agree that those two had no place in the fantastic 23rd century...
Timo Saloniemi
Spock knew when those guys got there, so he just beamed them back at the right time. Voilà. Piece o' pie; easy as cake.
