Even after McCoy says it, Spock replies, "My first command."---you can almost hear the ? at the end of the sentence.
Indeed. One can choose whether to believe that McCoy was being plain nasty and sarcastic ("You botched it all up despite having long experience with these things, just because you had to be you!"), or perhaps ignorant of Spock's track record (because while many of the characters are said to have long joint pasts, there's no direct evidence that McCoy and Spock would have known each other for long).
You don't serve 18 years and rise to Lt. Comm/Comm without leading a landing party---period.
...Unless you are an instructor for your entire career before this, like the parallel Spock from STXI.
But "our" Spock had field assignments with Pike.
That should really be Memory Beta suggesting - because these exact consequences were described in the Diane Carey novel Dreadnought!
where Boma reappears in a minor role.
On the other hand, Spock and McCoy together could have browbeaten the rest of the group to silence about what really happened, and no punishments of any sort would have been dished out. Scotty might be fuming, but it's not as if Boma insulted him personally or professionally. If Spock was okay with it, Scotty would have to agree to being, too.