John doesn't have a minority report per se. John asks if he has a minority report. He doesn't. There is no formally flagged disagreement or different point of view between the precogs, which would constitute a minority report. But John doesn't change his destiny or report, he fulfills it and the interpretation is wrong. It's a false positive like danny whitwer was talking about.
John doesn't shoot Crow. Crow had pressed the gun in to his own abdomen and pulled the trigger himself. As John steps away, the events or images from the prevision play out exactly as they were seen before, and they give the appearance that John killed Crow. Agatha wasn't wrong about her prediction, and indeed John didn't change anything. He fulfills the prevision by actually going to where it is supposed to happen, he does for a bit have the intention of killing Crow (this sort of trauma is what sparks the prevision), chooses not to and then appears to have killed him. The prediction was correct but the interpretation - that it's a murder - was incorrect. We don't see the whole picture from the prevision. John chooses not to Kill crow and Crow takes his own life all during the same traumatic event, thus making it seem to the precogs that he committed the crime.
This is exactly what Danny Whitwer was talking about when asking if they ever got any false positives. To paraphrase the "mother" of precrime, "the precogs are never wrong. However, they do sometimes disagree" They sometimes see things from different perspectives. That's called a minority report - but John and perhaps others only ever appeared to have killed a person when in reality they didn't go through with it.
So whether those wearing halos have a minority report out there where we have discrepancies or the precogs merely assume it's a murder because of an incomplete picture and it's violent nature, the whole program is fatally flawed.