An op-ed column does not speak for the newspaper it is published in. It's literally the opposite of the editorial board. Thus the name "op-ed."
Mueller never said there was no collusion. Trump said Mueller said there was no collusion. Barr's summary quotes Mueller's report as saying “[T]he investigation did not establish that members of the Trump Campaign conspired or coordinated with the Russian government in its election interference activities.” So they didn't find proof of collusion. That is not the same as concluding that collusion did not occur.
Barr also provides this other quote from Mueller's report: “while this report does not conclude that the President committed a crime, it also does not exonerate him.”
As far as I know, op-ed stood for opinon editorial. To say it is "opposite of the editorial board" doesn't make sense when the editorial board themselves contribute to the op-ed. For example, the editorial board endorsed hillary clinton on their op-ed. How could that possibly be "opposite of the editorial board"?
Also, david brooks is a well established journalist who has written for the nytimes for a long time. Not saying he speaks for The NYTimes but I'm sure he expressed some of their sentiments.
In our legal system, we have the concept innocent until proven guilty. "Didn't find proof of collusion" means there wasn't any collusion for all intents and purposes. To claim collusion without proof is partaking in the world of conspiracy theories.
As for Mueller's statement, of course it doesn't exonerate Trump. In order to be exonerated, you have to be convicted of a crime first. You are exonerated of convictions. You also aren't exonerated for russian collusion because you've never been convicted of russian collusion. Mueller's statement apllies to you, me and pretty much everyone on earth.
You make it impossible to have a logical and rational conversation because you've decided to reject logic and rationality for politics, semantics and conspiracy theory. This is why the surge of politics on social media worries me.
Mueller never said there was no collusion. Trump said Mueller said there was no collusion. Barr's summary quotes Mueller's report as saying “[T]he investigation did not establish that members of the Trump Campaign conspired or coordinated with the Russian government in its election interference activities.” So they didn't find proof of collusion. That is not the same as concluding that collusion did not occur.
Barr also provides this other quote from Mueller's report: “while this report does not conclude that the President committed a crime, it also does not exonerate him.”