On the basis of what the article says it sounds like he voluntarily dived into the water and this was not connected to the core training he was undertaking. He wasn't instructed to; he wasn't seemingly ordered to.
Notwithstanding the need for universal exped insurance to cover mishaps, there has to be a line somewhere limiting MoD liability for ancilliary injury; something along the lines of an injury in a car crash en route to the training, which the subject could not have anticipated or prevented, is covered. Anything action unattributable to the core MoD-sponsored activity, such as this apparently unsupervised and voluntary dive, isn't.
I'm sorry for the marine, I really am, but servicemen can't be expected to live in an impervious bubble of liability cover for their every action under the umbrella of 'exped', and must bear some personal responsibility for their actions, as they would in normal life.