I haven't read the BB essay in question, but I'm sure I've read the sutta and the footnotes of his sutta translation... coming from which, I take it that a wisdom-liberated arahant can become such without having to attain the 4th jhana... a lesser (sutta-defined) jhana will also do. Furthermore, in the Satipatthana Sutta there is potential promise of quick arahantship following the satipatthana method, but without any boilerplate text on the jhanas - the closest it gets to talk on samadhi is when the meditator tranquilizes the bodily formations through anapanasati, or when observing whether or not the seven factors for awakening are present.
Now I don't much fancy hunting around this long topic for the link to the post where I said, "Did all arahants attain to the 4th jhana? No." but if you are, and the above paragraph was insufficient for you, I'll be happy to explain the intended context further.
“I hope, Anuruddha, that you are all living in concord, with mutual appreciation, without disputing, blending like milk and water, viewing each other with kindly eyes.” (MN 31)
What is the final conviction that comes when radical attention is razor-edge sharp? That the object of the mind is mind-made (manomaya). (Ven. Ñāṇananda)
"If you have always believed that everyone should play by the same rules and be judged by the same standards, that would have gotten you labeled a radical 50 years ago, a liberal 25 years ago and a racist today." (Thomas Sowell)