Capn Bloggs
In listening to the audio, the second call to the Cessna shows an elevated intonation from the controller, a sign of at least mildly elevated urgency. The Captain of UA 889 called up and requested a discrete frequency to memorialize the event with a supe, and to support the FO flying. If he had "let it go" until later, he would have communicated to his F/O a lack of immediacy, as she was clearly upset, and rightly so. His action was entirely proper.
It could also be said that the Cessna was in a far better position to maneuver, the 777 has the priority. If there is fault to be found, I would assign a bit more responsibility to ATC for not including the UA flight in the "mix". However, I think the reporting is rather hyperbolic, and the News (animation) video is absurd.
imo,bear