It looks like Jesus’ “But I say” rule assumes that Torah, as interpreted by the Pharisees, covered acts and He was expanding the rule. However, since there was no “covering” for intentional acts some thought sin must have been intended.
Mat 5:20 For I say unto you, That except your righteousness shall exceed [the righteousness] of the scribes and Pharisees, ye shall in no case enter into the kingdom of heaven.
Mat 5:21-22 Ye have heard that it was said by them of old time, Thou shalt not kill; and whosoever shall kill shall be in danger of the judgment: But I say unto you, That whosoever is angry with his brother without a cause shall be in danger of the judgment: and whosoever shall say to his brother, Raca, shall be in danger of the council: but whosoever shall say, Thou fool, shall be in danger of hell fire.
Mat 5:27-28 Ye have heard that it was said by them of old time, Thou shalt not commit adultery: But I say unto you, That whosoever looketh on a woman to lust after her hath committed adultery with her already in his heart.
Job 31:1-4, I made a covenant with mine eyes; why then should I think upon a maid? For what portion of God [is there] from above? and [what] inheritance of the Almighty from on high? [Is] not destruction to the wicked? and a strange [punishment] to the workers of iniquity? Doth not he see my ways, and count all my steps?
Let's say, for example, that a man steals a sheep for whatever reason, then repents and wants to make things right. There's no way he "accidentally" stole the sheep, nor could he claim ignorance of the Ten Words, but neverthess the Torah provides a remedy: He must return the sheep and give another 20% of its value back to its owner; if the sheep was already slaughtered or sold, he had to pay back five times the value of the sheep. Only then, after making the matter right with his fellow man, could he go to to Jerusalem and make an offering to make things right with God.
The reason that the guy who gathered sticks on the Sabbath was killed was not simply for violating the Sabbath in a moment of weakness; it was because he did so in a situation where everyone was keeping the Sabbath together and right in front of the Sh'khinah, the Presence of God, which was visible as the pillar of cloud and fire over the camp. Just as you will punish your children more severely for open defiance to your face than for an error committed while out and about, so the Holy One dealt with him.
One of the reasons for joy among the disciples was the knowledge that though Israel as a whole had committed sin "with a high hand" over and over again to the point where the Sh'khinah twice departed the Temple, nevertheless the Holy One had provided a sacrifice that could and would restore Israel to full Covenant relationship with Him and allow her to inherit her promises.
Shalom.