I LOVED that - totally in keeping with Kirk's character IMO. It was so refreshing we didn't have to sit through a tedious conference about it - or some kind of spooky "spirit walk" with "prophets" etc....and massive violation of the Prime Directive at the start of the movie.
This.
And is it really that big of a violation to begin with? I agree with Kirk's assessment: they saw us, big deal. A few natives saw the Enterprise. For a while there will be stories about it among them. Then it will simply fade away with time.
And I'd rather watch Kirk save people than see Picard and his officers sit on their hands and mumble about a "cosmic plan".