But yeah, with Tomorrow is Yesterday, you're talking about a 1st season episode. You're going to have a lot of plot blatant plot devices floating around. I'll have to pull out my dvds and watch that episode again but for now I'm going to take Futurguy's interpretation of the events in that episode. TNG seems to suggest that transporting from a ship in warp is probably not done regularly if at all. The episode "The Schizoid Man" they use near-warp transport where the ships drops out of warp and then jumps back to warp just as the subject being transported is in the rematerialization phase.[/quote]
In TIY, the Enterprise was definitely exceeding even the warp scale of that time. She never slowed down while transporting Captain Christopher back to a point before he saw the Enterprise, same with the security guard.
I did have a though though that trans-warp beaming might just have been merely what described beaming a person or persons a (really) great distance, but Spock in STXI mentioned something about transporting aboard the Enterprise WHILE at warp (not possible at the time to Spock), which would sort of point to the fact (in reverse) of Capt. Christopher being beamed a great distance from a ship at warp. TOS did it "first" though as I mentioned, there did not seem to be any consideration as to its safety...lol It's as if that was an everyday occurrence or ability of the current technology, not necessarily of Mr. Scotts doing.
Now if he had spouted some tecno-babble of an experiment he was working on (TNG style) that would solve the problem of returning Capt Christopher to earth WHILE at whoop-azz warp, then I would concede to the fact that Scotty did invent it, but not enough information to give him (TOS) credit for the achievement.
Another point.......has anyone considered the possible connection of Capt. Christopher to Capt. (Christopher) Pike, as in a deeper connection to the real need to return (Pilot) Capt. Christopher back to Earth? A backstory that Spock would only understand and feel a need to see to it being done without appearing emotional? Could be a good story there, just not for the new-Trek.