The first thing to go through Mathew Vickers' mind when a 2-metre grey reef shark ripped into his arm was that it was statistically improbable.

"This shouldn't be happening," he told 7.30.

"I couldn't buy a lottery ticket that day but if I did, I most likely would have won."

"I looked at my arm, it was bleeding to some extent and a massive flap of skin was hanging off.

"It was 17 seconds from shark bite to stumbling upon the boat."

'Get out of the water because something's gone wrong'

Mathew Vickers with his arm strapped up after being bitten by a shark ( Supplied: Mathew Vickers )

Mr Vickers was a volunteer aboard a four-week coral reef research mission, funded and conducted by James Cook University (JCU) and their world-renowned coral reef studies centre.

At the time of the incident, he was snorkelling and filming underwater off Lizard Island in the Great Barrier Reef, while others in the group were feeding the marine life.

"My thoughts were, get to the boat," Mathew Vickers said.

"Get my arm out of the water, don't drop my camera, tell the rest of the people to get out of the water and that was it.

"That was my thought process: get everyone out of the water because something's gone wrong."

Mr Vickers was airlifted to Cairns Hospital, where he was met by his girlfriend Astrid Vachette, and received 90 stitches in two operations to save his arm.

"It was an accident, he still had two or three weeks to go, he was gaining so much experience. I think he was just annoyed by the whole situation of now he's in Cairns, trying to think about logistics," Ms Vachette told 7.30.

It was then his battle with JCU and their insurers over his out-of-pocket medical and travel expenses.

'Do not engage in activities that may attract sharks'

The grey reef shark that bit Mathew Vickers ( Supplied: Mathew Vickers )

Mathew Vickers was under the impression he was fully insured by JCU and their insurer.

The day after the incident, Mr Vickers received a reassuring email from the team leader of the research trip.

"Just spoke to JCU, you are all covered as I suspected, they will pay for everything until full recovery," his colleague wrote.

"I felt good that the university would have my back," Mr Vickers said.

But three days later, another JCU employee backtracked, telling Mathew Vickers that he had "a very limited level of coverage" that was "similar to that of a student who injures themselves".

To date, he says he has only received $555 from the university's insurer for his out of pocket medical expenses, which he says total up to $5000.

Volunteers and students in Queensland are not insured under WorkCover and it's up to JCU to investigate the incident internally.

Lizard Island Research Station's induction program says there's a moderate risk of being bitten by a marine animal, stating, "Do not engage in activities that may attract sharks".

But in emails obtained by 7.30, the team leader admitted that "feeding the beasts" was his idea.

"My idea and my execution, so my bad," the team leader wrote to Mathew the day after he was bitten.

"My other main fault was my naivety, that it was a harmless activity."

For his part, Mr Vickers, who said it did occur to him to take out his own insurance, said he does not blame the shark.

"In hindsight I guess I shouldn't have even been there on the day," he said.

"If you've never swum with sharks before I wouldn't encourage that."

To date, JCU has not granted Mr Vickers access to the report after his application under the Right To Know Act.

Reef volunteers

Mathew Vickers shows his shark bite wound ( Supplied: Mathew Vickers )

Mathew Vickers' shark bite has revealed more than just his flesh and bone.

It's revealed how some researchers on the Great Barrier Reef can be dangerously under-insured.

Unlike other states, Queensland doesn't cover volunteers in the same way as the employees they work alongside.

"The university, and universities everywhere, rely very heavily on volunteer culture. And people helping each other in their research projects," Mr Vickers said.

"I guess the hope is nothing goes wrong.

"They should ensure that the next volunteers are treated properly and never have to fall into the same situation."

James Cook University declined 7.30 request's for an interview.

However, they said they have reviewed the incident and are now considering how they might further support Mathew Vickers, including financially.

"The snorkelling activity was not part of the JCU field trip. Despite this, JCU has and is continuing to provide support to Mathew Vickers." a JCU spokesperson said.