Following Sunday's Bahrain Grand Prix, Jenson Button slated Sergio Perez as "dangerous" and "dirty", suggesting the Mexican would cause an accident if he failed to calm down.
Button was left fuming with Perez's driving as the 23-year-old first clipped the Briton from behind as he attempted to pass, losing part of his front wing, and then banged wheels with Button at high speed, with both fortunate to avoid a major incident.
Button twice went on to team radio to voice his anger and Whitmarsh has admitted to being badgered by his colleagues on the pit wall to bring a halt to the apparent madness.
But living by the creed at McLaren that both drivers are equal and free to race - unlike at Red Bull and Mercedes where team orders were issued in Malaysia and caused such a stir - Whitmarsh stood by his guns.
"I had a lot of noise in my ear, people saying 'stop this, stop this, it's hurting us', suggesting I stop them racing," said Whitmarsh.
"I didn't, and I know it could have gone horribly wrong. On balance it was the right thing - in the long term - for both drivers to know they are racing each other and are competitive.
"If you do that the driver behind is always going to feel aggrieved, so I let it go because we allow our drivers to race.
"To have said to Checo 'don't fight', or to Jenson 'yield, let your team-mate by', I've not yet done it and I don't think I'm likely to start doing it any time soon.
"It's not the first time I've had to make a decision like that. It's happened lots of times before. That's my job.
"Nobody is going to give an instruction like that to a driver without my approval, and that's how we go motor racing.
"Of course it's uncomfortable because you face a situation where, if they had taken each other off, I'm the one with microphones in my face, so that gives me the privilege of making the decision."
Whitmarsh at least appreciated the voices of concern around him as a fired-up Perez, after being told to "toughen up" the week before in China by his boss, crossed the line.
"The dynamics of this team - and not just the drivers but the race engineers, the strategists - is team Button want to beat team Perez," said Whitmarsh.
"I like that feeling, that right down to the mechanics, they want their car to beat the other car. That's how we work as a race team.
"It creates certain tensions in the system, but that's the right way to do it."
Whitmarsh could also understand Button's exasperation and comments in the immediate aftermath, and at one stage had a lengthy conversation with the 33-year-old in the middle of the paddock on the matter.
"If I was Jenson I'd be p****d off as well," added Whitmarsh.
"I wouldn't expect him to be overly happy because he doesn't want to be beaten by anyone, least of all his team-mate.
"But the two of them are good guys and they'll work it out. They'll be fine about it.
"The great thing about Jenson is he's a grown-up, he'll get over it, and they'll have a great relationship.
"He has a balanced, mature approach. He knows his team-mate has been under the hammer, is young, has had a bit of pressure, has something to learn and a point to prove.
"Jenson can stand back and be reflective. Very quickly he gets to that point because he is an intelligent guy.
"Jenson will get over it because he's a star like that."
That, though, was not Button's viewpoint as he told Press Association Sport: "I cannot retract my comments.
"It is great we have no team orders and are allowed to fight, we just have to respect that.
"But I feel Checo was a little more aggressive than he needed to be."
Asked whether the gloves were now off between himself and Perez, the 33-year-old replied: "Yeah, but I am not going to change my style of driving.
"I drive the way I think is the correct manner and the way you should to respect your fellow drivers."