No, they had no connection between Phoenix and the forgery, other than an anonymous, unprovable tip and his presenting it in Court. Misham only testifies to making the forgery and explicitly states he does not know who ordered it. Manfred Von Karma, in all of his slime, would never once have settled for that. There is no solid connection between Phoenix and the forgery. The previous case in this game makes a HUGE deal about decisive evidence being necessary, to the point where it requires a confession from Machi to equate. Decisive Evidence is always a recurring theme in this series. Hell, it's brought up several times in the first case of Apollo Justice. And Klavier lacked every last ounce of decisive evidence to tie Phoenix to the crime. He had no evidence, no witness, and an anonymous, unsubstantiatable tip. The system fails completely when it disbars Phoenix. Klavier has nothing to tie him to it, and the Judge is absolutely unwilling to listen to Phoenix's side of the story.
And all of this has happened just WEEKS after Miles Edgeworth has brought down the entirely corrupt Prosecutorial Investigation Committee. Phoenix says a miracle happened in the court that day, and he's right: It's nothing short of miraculous that everyone in the system, the Judge especially, could be so stupid and corrupt that they would disbar Phoenix. Hell, this is the Judge who is FAMOUS for handing down just verdicts. And what does he do? Not even bother to hear Phoenix out. The man has seen Phoenix bring down the Chief of Police, Manfred von Karma, Godot, and foil assassins and mass murderers and he won't HEAR his side of the story?
Like I said, it is no wonder Nick gets a little nutty after that.
I understand where you're coming from and you're right when you say the von Karma would never have settled for that, he instead would have forged his own evidence to prove it. But Phoenix himself had no evidence to prove that he wasn't the one who forged the diary page. The second the diary page was proven to be a forgery Nick was considered the guilty party. He was the one who presented it to the court and he had no proof besides his own words that he hadn't ordered it. Phoenix had a hearing after the trial where he would have had the chance to plea his case, but because he had no actual evedince otherwise everyone on the hearing comitee beside Kristoph declares him guilty. That's how the court system works in the Ace Attorney world, all suspects are guilty until proven otherwise.
The Steel Samurai case is a good example of this, Will Powers had no motive and it was proven on the second day of the trial that he couldn't have done it. But he was still considered guilty until Phoenix proved someone else had done it. Stupid as it is, Klavier didn't need any proof beyond proving that the diary page was indeed a forgery. It follows the logic of the previous games.
The Steel Samurai case is a good example of this, Will Powers had no motive and it was proven on the second day of the trial that he couldn't have done it. But he was still considered guilty until Phoenix proved someone else had done it. Stupid as it is, Klavier didn't need any proof beyond proving that the diary page was indeed a forgery. It follows the logic of the previous games.