Have you noticed that I have cited Luke 1:5-6 a half dozen times, but STILL, people seem to think that "no one is righteous, no one can keep the Law"... So much for respect for the Word of God when a manmade doctrine is at stake. Can't knock over the sacred cow, can we...
I have come to the conclusion that there were and possibly are, those you can follow the Law (every jot and tittle) as the scripture you post and as well we see in Job. Yes, Job was before the written Law but that is not here or there as certainly there was already sacrifices, caring for the poor, etc.
Months ago I felt the need to read Job again with hopefully more spiritual eyes than previously and the Holy Spirit did show me some things I had not seen before but until this morning I don't think I had a full revelation of what the verse He had shown me meant. I tied the verse to Job doing
works by his own hand, which is clearly a part of it but now I think there is more. Sometimes I am very dense.
Job 40:14
King James Version (KJV)
14 Then will I also confess unto thee that thine own right hand can save thee.
Job was found to be righteous and upright just as those in your Luke scripture. So why did God say this to him. In my blindness I saw this as Job doing these things by this own will and declaring himself righteous but that cannot be the only problem here. God in chapters 38-41 at least is pointing out to Job all the things that He, God, can and does do as the Creator compared to Job as the created . It is in this context that He makes the above statement to Job. If Job can do what the Creator does then God will admit to Job that he can save himself by being righteous as a man can be righteous. God says that he cannot be saved this way even though God Himself found him to be in complete obedience in every way.
We know that it is only by God's grace that we can be saved but what of righteousness unto justification?
Could it be that God's righteous is above the laws that He has given to man? Could it be that only the righteousness of God Himself is enough to save thee?
Could it be that only the Gift of Righteousness (the righteousness of Christ) can save thee? Which is bigger than the Law?
So in conclusion I would agree with your deduction that man can obey the Law, however he would still not be righteous enough for salvation.