I mean yes but no the salient point for the Chinese would be that the army did in fact not roll over all the students on the square, they "merely" intimidated them out of there after massacring themselves through barricades Peking locals had erected to protect the students. I say massacring not so much because those people didn't right-out attack the army, but because the fighting was completely one-sided we're talking pretty much fists and stones against machine guns and tanks.

There were plenty of people within the CCP who wanted to see much more blood, that there was so relatively little blood is thanks to Peking locals (this time less militant ones) bringing rice and fried noodles to the army camping out in front of the city while explaining to them that (unlike what they had heard from the party) those weren't counter-revolutionary bourgeois foreign agents on the square, but simply reformists.

That's why that point is rather important, the Chinese people might not be saying it out loud but "there was a massacre on the square" implies that the people did nothing to influence the situation. They very much did and avoided a much worse calamity.