That's a fair question since [MENTION=6792106]Sezarious[/MENTION] opened the door to it. I'd like to see what people say.
I think the answer to this is dependent on a much larger issue of group dynamics. To have or not to have hidden rolls is a pretty minor issue. I would never walk away from a group over an issue like that alone.
On the other hand, I might walk away from a gave a DM a really hard time about how he or she managed the finer points of the game's mechanics. Ultimately, that stuff is the DM's responsibility, and it is up to the DM to refine the specifics of their recipe for how they run a game that is as fair, immersive, challenging and enjoyable as everybody wants. If I suggested that a player roll was going to be made behind the screen, and a player said, "No way, I refuse to play that way," I would be concerned, because I don't want to have players constantly fighting me on how I mechanically run the game. At the end of the day, being able to be loose about the "method" and focus on the overall objective is much more important to me. As a player, I try to keep my mouth shut about that stuff as well.
Now, if I instituted secret rolls for certain things, and after a few sessions a player said, "You know, Red, that whole thing where you roll certain player checks behind the screen doesn't really work for me. Could you try and find another way to handle those situations?" I would probably say, "hell yeah, let's try something else. I'm not trying to make you play a game you don't like."
We rotate DM'ing responsibilities in my group, and these little variations come up all the time. I like to re-roll initiative every round. Another DM likes to read box text. Another DM likes to run a very liberal action economy. I roll most monster dice in front of the screen, and another rolls most of that stuff behind the screen. I never fudge dice, and hell, maybe the other DM's do. Some things get standardized as we, as a group, come to agree on a particular ruling, but we also all know that each DM is going to run the game the way he knows how to run it best, so we try not to backseat drive the whole time. If a group weren't willing to give me that trust and autonomy on tons of issues, I would walk away, yes.