No, but seriously, did you expect him to say that he left because of the management? I surely didn't.
That would be a slap in the face. Due to mutual respect I'm sure neither Conte nor our staff would want such statements.
You suggest this might be a made-up story (and Nedved is not the kind of guy that wants to be politically-correct), but the truth is that if you've seen Conte troughout the year it's not only probable, but pratically evident that he was really tired and needed a big rest. Just look at his face, the sound of his voice. Hell, he's even had signs under his eyes sometimes...
Don't want to exaggerate things, the point I want to make is that he is not the total IronMan someone depicted him to be. And Juve task in these 3 years was a tough work, with all the media going against you pratically, and he was even a bit of a fan, and for win 3 years in a row after the collapse of the previous Juve, he had to be always focused.
In the resignation video on Youtube, he says himself that was really tired... So, Nedved's story to me looks realistic.
But it's better to believe that he left for "Vidal and Pogba leaving"

, "the Iturbe saga"

(said also by some of those that considered Iturbe not ready and overpayed), "The board that was not ambitious"

(like if they can shit the money they need... And after all they've done in the last years under any point of view, facilities, social-media ideas, etc.) and other shit like that.