I suspect that we're getting part of the story.
I sincerely doubt the Capt did not go up through his chain of command, it's baked in his genes, and unless they have evidence that he sent the letter to the media its a typical Navy move. Could have easily been someone else on the cc line of his message that spilled it. There are no shortage of officers in the Navy who think their career depends on stepping on others.
If the CoC did blow him off and he felt he had no option but to go public, well, he knew he was going to fall on his sword and he can look in the mirror with pride that he did what he thought the right thing was.
Carrier CO's are not politically ignorant.
