That could be interpreted as "will it cause a schedule problem", or "is there another option I should consider" or "might this make it worse". Ultimately he never actually asks a question, just says what he's thinking about doing. To me it reads like the captain is keeping his superiors in the loop, but still has controll.
The problem with the response is that it has clearly been treated as a request ("diversion request heads up through Old Bahama Channel understood and authorized") that could have been denied.
It's obviously not an admission of guilt, but a red flag that's worth investigating.
As another said, the Captain didn't specify what the question was.
Saying "authorized" was a big mistake. I work somewhere now where I have to be careful using that word because it implies you're taking on the responsibility, and if something goes wrong through no fault of your own, the blame now lies on you where as it wouldn't have if you just simply acknowledged receipt of the question/statement.
>Question I would like to transit the Old Bahama Channel on our return northbound leg
He was clearly asking, not informing.