Pitman was close enough to know the exact time she went under, as he checked his watch and saw it was 2:20am.
The problem I find is that most people take what somebody said to be the absolute truth. But eyewitness accounts have proven to be not very reliable, especially when it comes to the sequencing of events or subject estimates of distances and time intervals. In the case of Pitman:
Senator SMITH. Describe, if you can, how she sank?
Mr. PITMAN. Judging by what I could see from a distance, she gradually disappeared until the forecastle head was submerged to the bridge. Then she turned right on end and went down perpendicularly.
Senator SMITH. At about what angle?
Mr. PITMAN. She went straight.
Senator SMITH. Right straight down?
Mr. PITMAN. Absolutely. That was the last I saw of her.
Senator SMITH. Did she seem to be broken in two.
Mr. PITMAN. Oh, no. Senator SMITH. Or was she entirely intact? Did you hear any explosions?
Mr. PITMAN. Yes; four reports.
Senator SMITH. What kind of reports?
Mr. PITMAN. They sounded like the reports of a big gun in the distance.
Senator SMITH. What did you assume they were?
Mr. PITMAN. I assumed it was bulkheads going, myself.
Senator SMITH. Did you hear anything like boiler explosions?
Mr. PITMAN. Yes; I heard a lot of people say that; but I have my doubts about that. I do not see why the boilers should burst because there was no steam there. They should have been stopped about two hours and a half. The fires had not been fed, so there was very little steam there.
Senator SMITH. Are we to understand that you do not believe that boilers exploded?
Mr. PITMAN. I do not believe it.
Senator SMITH. And from the distance you were from the ship, you would have known it if that had occurred?
Mr. PITMAN. I think so.
Others reported hearing sharp explosions before going under.
L/O Symons: "I stood and watched it till I heard two sharp explosions in the ship. What they were I could not say. Then she suddenly took a top cant, her stern came well out of the water then...You know what I mean to say, she took a heavy cant and her bow went down clear...Head down, and that is the time when I saw her lights go out, all her lights. The next thing I saw was her poop. As she went down like that so her poop righted itself and I thought to myself, 'The poop is going to float.' It could not have been more than two or three minutes after that that her poop went up as straight as anything; there was a sound like steady thunder as you hear on an ordinary night at a distance, and soon she disappeared from view."