Kirk is making an inspection tour when the movie gets under way, and all available evidence is that this is a perfectly reasonable and correct thing for the person overseeing training of a new crew to do. Granted Kirk probably takes more joy in this cruise being aboard the USS Enterprise than he would being aboard the USS Chuckles The Silly Piggy, but a ship of trainees going on a training voyage aboard a training ship is not a dangerous liberty.
Oh, the trip is certainly regulation-kosher and all that. It's just that it happens there and then specifically because Kirk wants to celebrate his birthday with his friends (including an old one made of duranium and tritanium) - which means that the mission is "Kirk's fault", in Scotty's eyes.
And the "dangerous liberty" is not the embarking on a training cruise. It is the turning of the training cruise into an operational sortie, for the apparent non-urgent goal of sorting out some strange bureaucratic problem the Admiral's old flame is having. of course, the liberty Kirk is truly taking is greater than that, as he apparently knows what Genesis is, and thus knows that the problem probably goes beyond bureaucracy and random comm troubles.
As for the redirection of the ship to Regula: yes, you've argued that Kirk must have nagged Star Fleet into sending him instead of the mythical other ship in the quadrant. What we actually do know is that Star Fleet orders Kirk to take control of the ship, and Star Fleet orders Kirk to investigate Regula One. There's no evidence that Kirk did anything deliberate to get this assignment other than pass on Carol Marcus's confused message warning of danger.
But how would Scotty see it? Scotty doesn't know Genesis is Armageddon. Scotty thinks Kirk is running to chat with Carol Marcus while Scotty's little people fix her subspace transmitter. When
that mission turns to mayhem, Scotty has a legitimate reason to be angry - at the mayhem itself, at the secrecy, at the deliberate putting of the cadets to that secret danger.
And Kirk certainly can't have maneuvered the Enterprise to be in interception range on the guess that something might happen over Reliant's way: they were following a training cruise scheduled before Reliant even got to Ceti Alpha.
To nitpick, the cruise wasn't exactly scheduled timewise, as it came as a seeming delightful surprise to Scotty. And it wasn't exactly scheduled coursewise, as Sulu was told to indulge himself.
Kirk wouldn't have needed to maneuver the Enterprise to being nearby anyway: Ceti Alpha was near the spot where the Botany Bay was discovered -- and that ship was travelling by very early drives requiring years to travel between planets -- and Reliant was able to get to Regula in barely enough time for the Project Genesis crew to evacuate.
The details of this could be argued, as the movie does insist that all the elements were out in the sticks and outside the range of a timely cavalry charge from Earth or from some other UFP asset. And specifically since the
Botany Bay cannot have gotten very far from Earth (about 100-150 lightyears at .45 c would nicely provide the time dilation that turns the closer to three centuries into the closer to two that "Space Seed" and ST2 dialogue insists on), this situation must be viewed as something of a coincidence or contrivance.
We know the sublight ship was off the beaten path. We have a reason to think Ceti Alpha was also off the beaten path, although Kirk may also have made a significant warp jump between the site of discovery and the site of banishment. And it seems Regula is relatively close to Ceti Alpha, although not so close that it would have been the first target of the
Reliant on their apparently long and boring hunt for a suitably lifeless world.
The Federation probably also deliberately placed the Regula One laboratory off the beaten path, of course, knowing what the Marcuses were doing. Which raises the question: was Kirk's ship really the closest - or just the closest ship that could be trusted with the volatile secret?
Secrecy and lying is the underlying theme of the encounter with Khan. The original banishment remained a secret, embittering Khan. Genesis was a secret, too, as were its associated risks. This combination of cabals was intimately tied to Kirk, and came as a rude surprise to many, but Scotty really got the worst of it. He didn't deserve that, and neither did Peter Preston, which still makes me think Scotty would have been acting completely in character when coming to accuse Kirk of the death of his nephew (or even of his favorite apprentice, if we deny the familial relationship).
Timo Saloniemi