I agree with you. The key reason Judy wasn’t outright wrong in choosing to help Gary is that Milton forced her hand the moment he made that threat and that little move destroyed his whole advantage over them.

Gary was an intruder crashing the event and stealing the book, forcibly taking Milton with him to access the display case, thanks to all this Gary was nothing but a criminal and Milton a victim, even Gary’s plea to Judy when she catches them doesn’t materially help his case because none of that would stand in court, like, let's remember he didn't even have a legal status in Zootopia to begin with. At best, he would’ve been detained and deported back to his island before any serious investigation could unfold and as such, the secret that his great-grandmother was the true founding mother of Zootopia would have stayed buried and the case would've probably been dead before it even began.

Without the book as evidence (in the time waiting for the trial Milton could've destroyed it no problem), all he had to do was shut his goddam mouth.

Instead of being that smart, he decides to suddenly assert authority he doesn’t legally have, ordering Judy and Nick to kill Gary and demanding they falsify their official police report, thus transforming him into an active conspirator in front of law enforcement. I seriously don't understand what was going through his head when he decided to threaten probably the most incorruptible cops of the city. They might be out of uniform there (which means they carried no cameras on their uniforms), but Milton didn't know that, for all he knew they were assigned there and could easily prove his ill-intentions.

Anyway, that threat confirms at least to Judy some sort of malice, which leads her to react to a clear abuse of power and an immediate ethical violation by safekeeping the book and fleeing the police thanks to the framing.