From the perspective of the Navy and the Coast Guard, yeah, they heard a loud noise just after the mayday call. Anybody with both of those pieces of information is going to think it's pretty likely that the Titan failed catastrophically. But, "pretty likely" ain't really good enough, they needed to go out there and find concrete evidence of what happened. Until then, there is a chance that the noise was a coincidence. Like many folks upthread have said, if they called off the search as soon as the loud noise was heard, would the public be satisfied? Would the agencies be satisfied with themselves? Of course not
From the perspective of James Cameron, and the information available to him at the time, I think he put 2 and 2 together the next day, just like he said. But, notice that he did not walk around saying so right away. This is for exactly the same reason as the Navy and Coast Guard: a hunch, even a strong hunch, is not enough to call it while an international search is ongoing. If he had leaked his info out to the wider populace, would the outcome have been better? I think not. He was not certain, he was just "pretty sure." He made the right decision to keep his mouth shut publicly until the sub was found
As for how this was reported. Journalists do the best they can to achieve their goal of understanding the information and spreading it around. Their employers do the best they can to achieve their goal of selling consumers' eyeballs to advertisers. It's far from perfect, but it's the system we have
This is really not the topic to be bringing up unrelated debates about current and past politicians. Not sure how we got to that point after a good 40-odd pages of discussion on the lost sub. But I suggest that we try to stick closer to the topic at hand, fun as it is to throw a curveball into the mix