"...faithfulness cannot be determined only by what one does. The faithfulness that our Lord seeks from us is that which adheres to the things he believes, the things he values (because one can have faith in anything). If we want to be found faithful, our loyalty, our faith, our direction should be to do and practice what he has told us, to love one another even as he has loved us. And in order to do this, we need to keep looking at him as we are dealing with others..."
Faithfulness has a lot to do with obedience. They're not identical since, as aGuest mentioned, a person may have problems (in comprehension, in situation, etc.) which stand in the way of doing as the person may desire, that is, to obey, to be obedient.
This is a huge issue in my own experience, "thanks" to the dubs. How to keep loving people (even close family members) who have shown themselves more "faithful" to organizational teachings than to the God that organization claims to represent?
I remember a long-running debate among a group of dubs many years ago: Which is more important, loyalty or obedience? This thread seems to me to be along the same line.