Mark 2: Understanding the law

One Sabbath he was going through the grainfields, and as they made their way, his disciples began to pluck heads of grain. And the Pharisees were saying to him, "Look, why are they doing what is not lawful on the Sabbath?" And he said to them, "Have you never read what David did, when he was in need and was hungry, he and those who were with him: how he entered the house of God, in the time of Abiathar the high priest, and ate the bread of the Presence, which it is not lawful for any but the priests to eat, and also gave it to those who were with him?" And he said to them, "The Sabbath was made for man, not man for the Sabbath. So the Son of Man is lord even of the Sabbath."
(Mark 2:23-28 ESV)

I was having trouble understanding the point Jesus is making about David breaking the law and how that relates to what is right on the sabbath. My friend Tom was pointing out that Jesus is as usual pointing to the heart of the law and giving us a new understanding which is in line with the way we were created from the very beginning. For example the sabbath was made for man not to keep him from eating but to help man devote himself to The Lord. The same story from Matthew helped me understand a little more:

Or have you not read in the Law how on the Sabbath the priests in the temple profane the Sabbath and are guiltless? I tell you, something greater than the temple is here. And if you had known what this means, 'I desire mercy, and not sacrifice,' you would not have condemned the guiltless. (Matthew 12:5-7 ESV)

I don't really know where this idea came from but I was thinking of the way Jesus redefined our work when he came bringing the kingdom of God. Before Jesus the people of God were to work to bring in food and be fruitful in descendants by blood. But Jesus says our new work and food is to do the will of God to make disciples of all nations sharing the gospel expanding the kingdom not by blood but by the gospel. God is becoming a father to many sons and daughters through adoption by the Spirit!

The disciples and Jesus are bringing in the kingdom and so their work is spiritual 7 days of the week not just one day as the sabbath used to be. David also was bringing in the kingdom and facing persecution from the world so God provided food for him even if it was not lawful.

My understanding of this could be totally wrong and if so God I pray you guide me by your Spirit to the truth and not my understanding.
Amen