Although the Formula One title has eluded the duo in that period, with Red Bull's Sebastian Vettel taking the crown, there has been no animosity between the pair at any stage.
That is despite Neale giving Button a forthright answer when asked a direct question on the day he pondered whether to join McLaren just over two years ago after becoming champion with Brawn in 2009.
"When I met Jenson for the first time he was trying to weigh up what he was going to do and whether he would be interested," said Neale, speaking at the Autosport International Show.
"So I walked him around the Technology Centre on a Friday evening, just the two of us, most of the people had gone home by then, and he asked me directly 'Is this Lewis Hamilton's team?'
"And I said 'Yes it is', but there's no reason why it can't be your team as well because it had been Kimi's (Raikkonen) team, Juan Pablo's (Montoya) team, Fernando's (Alonso) team.
"That's because this organisation loves winners. I wasn't going to duck the issue, that Lewis had been with the team for a long time, was held in high regard and was part of the family.
"But certainly it was about making Jenson feel that if he came to us we would give the same commitment and effort to him because we love winners.
"One thing that has surprised me has been how ready and hungry Jenson has been to learn.
"If you read some of the press it comes across Jenson is mature, he has been world champion, and can now afford to be one of the senior statesmen in Formula One.
"But anybody who has worked with him will know just how demanding he is.
"He may be media savvy, friendly and at ease with himself because of the journey he has had.
"But he is fiercely hungry and developed enormously as a driver the last two years he has been with us, and he continues to push."
Asked whether he was surprised at how well Button and Hamilton had worked together, Neale replied: "The honest answer is yes."
Neale then highlighted the differences between the pair when it comes to simply setting up the car.
"Lewis is a force of nature - very driven, very passionate," said Neale.
"He will spend ages setting the car up to get the balance he is looking for, and then unwind all that during qualifying, just to get the car to slide and to give him the feeling he is on the edge and likes the car quite loose.
"Jenson's whole attitude is quite different, in that he is much more precise about things, that he does not like that degree of raggedness with the car and around him.
"But we like that difference. It brings something else to the team.
"They've also incredibly high regard for each other, and there is no animosity towards one another."
Crucial for Hamilton this season will be responding to being beaten by a team-mate for the first time, as was the case last season with Button, since he started single-seater racing.
In conjunction with all his personal problems behind the scenes, the forthcoming campaign is a crucial one for the 27-year-old.
Neale said: "Drivers don't like being beaten by their team-mate, and world champions don't like being beaten by anybody else either.
"Given the nature of Lewis being a fiercely competitive and driven individual, that was never going to sit easy with him.
"But it certainly wasn't an annus horribilis for Lewis by any means because we did win multiple races, but by his standards and ours it was a year for some learning and reflection.
"A lot of work has gone on over the winter to build a car to enable both guys to come back and get the job done, and for Lewis a chance to reflect on 2011 and come back as the man he'd like to be."