We can become sinless

I so often hear people say that we all will keep sinning because we are fallen and the natural man is an enemy to God. Also John is quoted that all HAVE sinned. But Mosiah 3:19 says, "For the natural man is an enemy to God, and has been from the fall of Adam, and will be, forever and ever, unless he yields to the enticings of the Holy Spirit, and putteth off the natural man and becometh a saint through the atonement of Christ the Lord, and becometh as a child, submissive, meek, humble, patient, full of love, willing to submit to all things which the Lord seeth fit to inflict upon him, even as a child doth submit to his father."
This, to me, poses that we can put off the natural man. Sometimes bad thoughts may cross my mind, so is this sin? Doesn't Satan tempt us? It surely can't be sin because Satan throws silly thoughts at us. Wouldn't it only be sin if we accept and go on with these thoughts as our own? It seems to me that sin would require an actual transgression of the law by us ("..For sin is the transgression of the law" 1 John 3:4).