Looking back, I think we came a lot closer to an all out boarder war than most realise.
The commander level agreement from the 6th of June would have been seen as a huge positive step by the PLA at easing tensions. But the provocation and attack lead by the rouge colonel so soon afterwards would have utterly destroy all trust and goodwill India might have had from the PLA.
That is extremely dangerous and significant, because if the Chinese no longer trusted anything the Indians had to say, then that drastically reduced the means of effective communications while magnifying the possibly of misunderstandings exponentially.
I think when the PLA force commander learnt of the attack, his first act would have been to put his entire force on high combat alert, as under those circumstances, he would have to conclude that the agreement from just a week earlier would have been a deception, and the only reason for the Indians to make such a move is to try to lure the PLA into letting down their guard for a sneak attack.
At the same time he would have passed on all that information up the chain of command to Beijing, who would have reacted with fury at the Indians and made the depth of that feeling known to the Indians through diplomatic channels, as well as a clear and final warning - you have deceived us, and you have launched an unprovoked attack that we consider a clear sign of hostility, this is your last chance to change course. Any more signs of aggression will be met with the full might of the PLA.
I am not sure if there is a hotline between the Chinese and Indian force commanders at the front, but if there is, the PLA force commander would have also convey that final warning to the Indian force commander.
I think this realisation of just how close they came to the brink is what cowed Modi so much, which was pretty clear from his public announcements surrounding the issue since.
The need to not show any more moves that could possibly be seen as further signs of treachery or aggression by the PLA could also explain how those 17 other Indian soldiers managed to die from exposure overnight, and why no Indian search and rescue effort was made to recover them until the next morning, after the Indians have gotten effective permission from the PLA to go recover their dead.
The heavy PLA helicopter sortie rate observed in the aftermath of the clash could thus be viewed in a different light - those weren’t medevac missions going in empty to take casualties out, but rather helicopters going in fully loaded with PLA rapid reaction forces deploying to reinforce frontline boarder troops, who would have been equipped for normal patrol duties and not heavy combat. These reinforcements would have been equipped for actual combat, and probably would have contained significant special forces elements.
My guess is that a combination of frantic Indian diplomatic assurances; a total freeze on Indian frontline military activities (verified by PLA special forces recon teams); and interviews from captured Indian officers gave the PLA enough assurance to believe the Indians claim that this was the result of rouge officers and not part of some grand scheme by India to try to launch a sneak attack, thus allowed tensions to ease.
Of all of the above, the fact that the Indians were prepared to let their men die from exposure rather than try to recovery them would probably have been the most convincing to the PLA that this really was a rouge op, and that they Indians are serious when they said they didn’t want a fight.