The race, the last event before the Formula One summer break, was won by Daniel Ricciardo of Red Bull and featured a compelling series of crashes, although Mercedes stole focus by instructing Hamilton to allow his team-mate to pass him on lap 51 as the drivers were following different strategies.
The Englishman refused to yield his position - the pair were third and fourth at the time - and instead fought on to claim a post on the podium after finishing in third behind Fernando Alonso. That had seemed to be a cause for celebration given that Hamilton started from the pit lane after a fire during qualifying caused extensive damage to his car, with a spin on his opening lap also resulting in minor damage to his front wing.
Yet Mercedes have instead been left to deal with the bad blood between their two drivers. Hamilton's third-place finish has enabled him to move within 11 points of Rosberg in the overall classification with just eight races left in the season. Had he followed orders and let the German pass then his pursuit of the drivers' championship might have come to real harm.
It might follow that Hamilton ignored his team in order to deny Rosberg a victory, although the greater issue is perhaps that he went against the wishes of Mercedes, who pay his wages. The Englishman was in little mood to apologise last night, however, since he retains ambitions of winning the title.
"I was in the same race as him," said Hamilton. "Just because he had one more stop than me doesn't mean I wasn't in the same race as him. Naturally, if I'd have let him by he would have had the opportunity to pull away, and after his pit stop he would have come back and overtaken me.
"So I was very, very shocked the team would ask me to do that, to be able to better his position. To be honest he didn't get close enough to overtake, but I was never going to lift off and lose ground to Fernando or Daniel to enable him to have a better race. So that was a bit strange."
The calculation came from Paddy Lowe, executive technical director of Mercedes, with the directive passed on to Hamilton by his race engineer Pete Bonnington. Toto Wolff, the team's executive director, conceded that he and Lowe will sit down with Hamilton and Rosberg to discuss the situation and it is understood that officials will be told never again to issue such a command to either man.
"We need to analyse how we ended up at that situation and whether we need to discuss the racing between the two," said Wolff. "It is getting intense and it is clear they are direct competitors for the world championship, so we need to sit down and discuss it.
"If Lewis had let Nico go, Nico could have won the race, but as a racer, a driver, I can understand why Lewis didn't obey. I could have gone on the radio, or Paddy could [to insist a move was made] but we didn't. I don't want to play the vicious general and demand they obey rules.
"Maybe what we decided at the beginning of the year doesn't function any more and now we cannot ask either driver to give up positions or jeopardise their championship chances for the benefit of the team."
Rosberg welcomed the prospect of discussing the situation with team officials and is expected to fight his corner. "We have to discuss it internally," said the German, who took fourth place at the Hungaroring.
"I don't want to speak theoretically about that situation, or what if and what people were thinking. It's better to discuss it in the team. I'm going to sit down with the team, Lewis will be there also, and we are going to go through everything."