Just to interject, the prime directive as stated by Kirk in TOS says that starfleet officers will give their lives to preserve it. We've seen Spock, especially, balk at shooting a phaser in view of natives, let alone flying a starship over their heads.
I tend to agree with most of what's been said in this thread but that bit seems to have not been mentioned.
The reason why no one mentions it is because it's from The Omega Glory, an episode whose ridiculousness has been acknowledged by many, and the fact that it never comes up every other time they argue about breaking the Prime Directive.
That said, if AbramsTrek went down that hardline route, it would explain why Kirk would bother lying about the whole Nibiru thing. He'd probably be demoted for not
letting Spock die and
saving the primitives, so lying about it would keep him out of trouble. Hell, the novelization seems to go with that take:
Chapter 4 wrote:
“What?” Kirk gaped at him. “Oh, come on! You gotta be kidding me! No, no—maybe you’re right. I could’ve been kicked out of Starfleet altogether, right? Parsing the Prime Directive, that’s a dismissal charge. Except that it resulted in saving a burgeoning civilization from being knocked back in development a couple of thousand years. Ordinarily that’d be reason for praise and promotion. It might’ve been, too, if the whole business had been left alone for a while. Things could have been mentioned through channels, revealed quietly a little bit at a time. Starting with the xenologists’ news of the good that we did would have percolated gradually upward through Starfleet. Words would have led to papers, papers to discussion of an exception. But, oh, no, there’s no room for patience in the mind of certain officers. It’s all gotta be reported right away and by the book, or not at all.”