I seem to have gained a reputation among my players for running tough-but-fair encounters. I stopped using screens a while back because I don't want the players thinking I'm fudging anything. In fact, I never fudge rolls -- if the players are in over their heads and I believe it's my fault, I'll have the monsters make tactical errors (usually provoking more opportunity attacks). Of course, the flip side of that coin is that when I believe the players are dying because they've been foolish or careless, I'll go ahead and kill them.
Setting aside the conceit that fudging monster/NPC behavior is somehow better than fudging rolls...
Using a screen, for me, isn't about hiding rolls*, it is about keeping my GM's notes out of sight, and having the added space for reference material for the GM.
*Though, it does make some rolls that *should* remain hidden, because the players don't know what they are about, out of sight.