I use the phrase "2 trains of thoughts" because Jesus approached the Sabbath totally different than the religious leaders of the time. If you read about Jesus and the Sabbath, he didn't follow the "letter of the law" per se. He healed, his disciples picked grain, and even said that the Sabbath was made for man and not the other way around. This conflicted with a lot of what people believed at the time.
Actually, the Pharisees position on the Sabbath is very complicated. In Ezekiel 20 we read something that is important to keep in mind...
Eze 20:23 I lifted up mine hand unto them also in the wilderness, that I would scatter them among the heathen, and disperse them through the countries;
Why was God going to do this?
Eze 20:24 Because they had not executed my judgments, but had despised my statutes, and had polluted my sabbaths, and their eyes were after their fathers' idols.
There were two sins that Israel had great problem with, idolatry and Sabbath breaking. The knee jerk reaction upon returning to the land was to build a fence around the Law. Their idea was not to build a fence at the cliff, but that they would keep people far away from the cliff. For an example, read the account in Mark 7 adn notice how many times Christ mentions the traditions of men and the commandments of men.
Now to Mark 2...
Mar 2:23 And it came to pass, that he went through the corn fields on the sabbath day; and his disciples began, as they went, to pluck the ears of corn.
Mar 2:24 And the Pharisees said unto him, Behold, why do they on the sabbath day that which is not lawful?
Mar 2:25 And he said unto them, Have ye never read what David did, when he had need, and was an hungred, he, and they that were with him?
Mar 2:26 How he went into the house of God in the days of Abiathar the high priest, and did eat the shewbread, which is not lawful to eat but for the priests, and gave also to them which were with him?
Mar 2:27 And he said unto them, The sabbath was made for man, and not man for the sabbath:
Mar 2:28 Therefore the Son of man is Lord also of the sabbath.
The accusation was that the disciples were harvesting and threshing grain on the Sabbath. Christ understood that there was a vast difference between picking a few heads of grain and rubbing them to remove the chaff and going out into the fields adn harvesting your crops.
Did they really violate the Sabbath Law? No. Did the violate the traditions of the Pharisees? Yep, and that was the problem, the Pharisees could not distinguish, they had no ability to see the correct application of the Sabbath Law.