According to Chester Nimitz's own evidence at Nuremburg (which he made in Dönitz's defence!) it had been decided already by the US high command that any exposed U-Boat represented a legitimate target, regardless of what it was doing and even if it meant "collateral" casualties in the case of allied survivors in the vicinity. This rings true - the Americans weren't much into the "manners" of civilised warfare from the outset, as was evident in pretty much their entire military strategy in land, sea and air.
The British interception of the message and how it was misinterpreted is not a version supported much by British historians or in British memoirs of those involved. This therefore appears to have been originally an American interpretation, subsequently cited by American historians, of part of Nimitz's testimony at Nuremberg when he explained that it was immaterial what the British or anyone else might have sent the US Air Force regarding the status of the U-Boat as it was not the job of the Air Force to abide by any maritime conventions, and even if it had been a US Navy bomber the outcome would probably have been the same. The "extra two days" in this version seems designed purely to absolve the British of all complicity in the event, even through blundering or deliberate procrastination on their part, and to emphasise that it was their American ally therefore who had acted unilaterally and by its own rules. This hard-line approach at Nuremberg was possibly taken to forestall any possible war crime accusations against the same navy in its conduct of the Pacific War against Japan, which at that time was still being considered a very real possibility in the aftermath of VJ Day which was still only three months beforehand and where conduct assessments by several international bodies were still underway.
The "truth" - for what it's worth in these cases - is probably that Hartenstein indeed behaved honourably - the British at least had evidence that he did, so that much is pretty certain - but that once the coordinates were relayed to the US Air Force base the U-Boat was doomed. Nimitz made no secret of his disgust with Hartenstein during his evidence, stating that the commander had behaved naively and even stupidly in engaging in an activity indistinguishable from a ruse to entrap allied forces, and that Dönitz's subsequent decision to abandon rescue attempts afterwards simply brought Germany in line with American policy in this regard. The British, who still seemed to believe in a notion of "fair play", were therefore equally stupid by the same token - hence the convenient invention of a crucial time delay (largely from American historical accounts) on their part in relaying the message to absolve them from blame by their "friend". What doesn't add up in the American official account is just how they apparently received coordinates exact enough to dispatch a bomber with this specific task to perform two days before they allegedly received the intelligence from British sources. As far as I know that has never been "explained", even mendaciously.