Too often, I find that when the GM says, "roll and we'll find out", it really means:
"If you roll pretty high you'll be able to do it. If you roll kinda low, you won't."
The reason I hate that kind of GMing is that my stats soon become meaningless. The success of whether I accomplish something or not is determined by what the d20 rolls, not what my abilities are compared to the d20.
that's a very specific kind of GMing, one which I tend to frown upon. Call it "storytelling" or "fudging" or whatever, it's essentially cheating in favor of the GM's personal preferences. I don't think a lack of transparency at suggests a need or desire to fudge - though the temptation might be there.
Let the numbers hold and let the dice fall where they may, I say.