Wellington swimmer Clareburt, who won two golds and a bronze at the Birmingham CommonwealthGames, is still unsure how to fund his buildup to the Paris Olympics.
His coach Gary Hollywood believes Clareburt can become a world star. Yet swimming's new poster boy would be in strife without private funding, and they struggle to find a pool with enough lane space for his world-class charge.
Butterfly ace Burmester, whose stellar career included a fourth placing at the 2008 Olympic games, said Clareburt's situation sounded familiar to what he experienced.
He sees the difficulties involved for a small isolated country like New Zealand competing on the world stage, but wants the high performance funding system overhauled.
Each sport relied on the results of a top athlete such as Clareburt to get good funding, but the athletes didn't reap enough of the benefit, he said.
"The national sports organisations for a long time have been forced into this system by High Performance Sport, the bit that is really broken," he said.
"Gary is pointing his finger at Swimming New Zealand, but I believe it starts from higher up, in the way High Performance Sport creates funding and treats athletes.
"I've looked at it for a long time and criticised them in the past, and again with the wellness stuff which is coming out.
"The money … is based on the results that the top athletes have. My results and Lewis' results would mainly determine what swimming gets, administration costs and everything else.
"But Swimming New Zealand doesn't count Lewis as an employee so Lewis doesn't get the credit he deserves for the funding he has brought in. That's the way HPS is set up. I was the same, and so were other athletes of the time."
Burmester says athletes' success often contributes to high performance funding, but they don't always receive their fair share while "all the administrators and CEOs stay exactly what they are on".
"Living allowance (payouts) that they pass on are a pathetic amount.
"I've always said that if you take away the coaches and athletes, there is no reason to have national sporting organisations. The swimmers and coaches are there and they will always carry on and do their best."
During his career, Burmester had stints in America where training comrades included Michael Phelps. But as a guest he was denied the use of aids such as stroke and speed analysis for money reasons.
Burmester said he was fortunate with the help he got from family, friends and businesses in Tauranga during his career, and they continued to back him when he shifted to Auckland's high performance swim facility.
But Auckland was an even tougher place to survive because athletes did not have familiar connections that can be so important.
And Burmester said the 23-year-old Clareburt's battle for training space in crowded lanes was even tougher for a butterfly swimmer, because of their wider wing spans.
"It is always difficult in a public pool because under bylaws there has to be a certain amount of public access, which is fine because ratepayers are paying," he said.
"He's in a 25-metre pool in a lane with six swimmers which is not ideal … similar to when I was growing up. You are constantly giving way.
"The argument is why doesn't he shift to Auckland, but maybe his support crew doesn't want to shift. There's no easy answer.
"Gary (Hollywood) isn't wrong in what he's saying, but how do you fund it?"
Burmester said if there was an answer, it lay in the bigger picture of the high-performance funding system.
And even with all of the disadvantages, Clareburt could succeed at the highest level if he was given the bare essentials.
"We have capable people in New Zealand but they don't have all the tools," said Burmester, a world short course and Commonwealth Games champion.
"Ultimately it comes down to pool space and competitions, which is what Lewis needs."
Butterfly and medley swimmer Clareburt was a Kiwi star of the Games, breaking a long gold medal drought in the pool.
But even attending a vital camp in Florida remains in doubt for financial reasons.
Hollywood says swimming may be doomed to become about participation rather than excellence.
"All the conversations are around participation," he said.
"People like the medals but I'm not sure they like to support it. We need these performances to inspire the next generation."