What is your definition of policing? If those FBI agents had been individual citizens who found misinformation and hit the report button, little different would have occurred. They got to cut the line, perhaps, but I doubt it would be much ahead of organizations like Microsoft, Stanford University, or the Archdiocese of Boston, to name some random bigwig organizations who could potentially complain to Twitter about something on Twitter.
I have a really hard time believing Twitter would have reacted in similar way if an individual or company initiated the same takedowns
You bet your ass they would if those individuals were celebrity influencers. Or if those companies were advertisers.
Twitter needs such entities to survive. Displeasing then is more existentially threatening than running afoul of the FBI.
As the source of multiple such requests to Twitter I guarantee you that they would.