For me personally, being an interpreter and not a creator of musical compositions, means trying to understand the ideas, and then try to bring that across. Not only do we have other instruments today, but these instruments vary also, as do the acoustics of the venues. So you try to make a piece come alive there and then, using your ears, mind, heart, fingers.
Leaving the urtext issue aside, I also think you need to be sensitive to what the writing tells you about the composition and the composer. I, for instance, think that with Mozart you have more freedom than with Beethoven. For many reasons. And I beleive it's in the character of the music itself.
Let's not forget that they themselves also experienced different instruments and halls, and I can't imagine that any of the great composers from the past would have played their own pieces exactly the same twice. First of all, it's physically impossible to exactly replicate a performance, second, I can't imagine they would have been really interested. Thirdly, when their own contemporaries/family/friends played it must have sounded different. Were they all wrong too?
Recordings can be a bit of a danger in this regard as performers can risk loosing their own original line of thought and understanding and opt to become copycats instead.
No good!:)
A healthy doubt is always a better way to go, 'cause if you start to doubt, you start to wonder, and if you start to wonder, you start to think. And then you're off!