I don´t understand, why you are so focused on the calculations.
From what i read:
a) we don´t know the starting pressure (so everything is just an assumption)
b) the statement was, that at the time of ascent to discuss the laughing issue they were at 4m depth. I did not find that 4m was the average or max depth for this first part of the dive (please correct if i missed it)
c) we don´t know if the brief surfacing to discuss the laughing issue was counted in the following dive time.
d) when the instructor realized, upon planning to end the dive, that a diver was missing, he returned and started a search. So this time should clearly not be considered as pre-planned, when discussing if the dive was planned proper.
So for me there is way to much assumption in any given scenario.
The notion is that the instructor screwed up by treating his DSD clients like they were OW students or certified divers. Without all the details it is nigh impossible to make accurate conclusions of what exactly happened. But one can draw some conclusions based on the details that the instructor provided.
One dead diver found under water at @6meters. Given the details in the instructors statements it would not be unreasonable to think the diver got separated from the group and ran out of air and drowned. While the starting pressure is unknown one can make some inferences based on the common types of tanks used in that area and common fill pressures, coupled with the fact that most people new to underwater exploration do not have good air consumption rates....add in some anxiety that one can draw from the fact that the instructor had to surface with the student because they were experiencing water in their regulator while they were laughing under water, and it is possible to infer that the deceased diver may have used up the last of her air supply after becoming separated. Again this is just speculation, whether it is what actually happened or not, the bottom line is that the instructor screwed up and lost his client who was found dead shortly after he surfaced with the other clients.
It is also possible that a meteor fell from outer space and hit the diver thus killing her and nobody else noticed it....Occams razor postulates that "when one hears hoof beats, one should look for horses not zebras".
This also supports the narrative introduced by Ian Yarwood that highlights there may be systemic issues on Koh Tao with regards to the general mentality towards safety. Losing a DSD client is, to me at least, definitively a sign of either poor judgment, a poor attitude towards the safety of ones clients, or both. The fact that the DSD client died is tragic and the sad thing is the only reason why this incident has really received any attention is because of the death of the DSD client. Had that not happened this would not be on anyone's radar to discuss....but the discussion should not be on the death, it should be focused on the avoidable events that happened before the death, so that divers can learn from those mistakes, and folks reading through all of this could make an educated choice as to whether or not they want to vacation with that operator/instructor in the future.
-Z