Because I Choose To, Because I Can

Isaiah chapter 64, verse 6 informs me that "Our good deeds are as filthy rags" to God. Put simply, it states that without belief in God, trust in God, nothing that we do can be considered good.
Now I'm no angel, and I'm no moral leader, yet even to me that verse seems off kilter. Does it really mean what it says? Can nothing be good without first off doffing our caps to the Lord?
Many years ago I was in London with a friend who's name I won't venture. We were drunk, although I was marginally less so. Anyway's, courtesy of some dodgy pizza eaten in Camden town my buddy decided to show us what an extreme anaphylactic reaction looks like. His eyes turned to slits, his face bloated outward, and his windpipe began to constrict. Godless drunkard that i was i decided to stand in front of an oncoming bus, which kindly stopped. The driver took one look at my friend, let us aboard, and delivered us to the nearest hospital whereby treatment was administered and, without being too dramatic, a life was saved. Some years later I was at my parents house and My father, as only he could, decided to demonstrate how to choke on a piece of cooked chicken. He collapsed and was going into panic, so I stuck by fingers down his throat and retrieved the offending obstruction, leaving Dad to recover over the course of several minutes.
That's two lives saved. I seek no credit for either, but use each account by way of example. Two deeds which played a part in keeping two human beings alive. Do these sound like filthy rags to you? Am I really required to fawn and grovel at the feet of an imaginary bronze age thug in order that those two actions be deemed good? I do not think so. Rather, it seems to me that the choice to pursue goodness is available to us all, irrespective of what we believe. Surely the truth of our character is measured in the integrity of our character rather than decided by the simple practice of belief?
I won't always do the right thing. I won't always want to even though I know I should. Yet this much I know; on the rare occasions when I'm not acting like a barbarian, and when the better angels of my nature compel me to reach out with mercy and bravery and compassion, I will do so not because I'm seeking the approval of God, but because I choose to, and because I can.