Yes they were not breaking the Sabbath in Jesus eye. They were not working on the Sabbath by just eating corn directly from the field. It is lawful to do good on the Sabbath day. You are lacking understanding about the Sabbath. It is one of Gods 10 commandments that gives us the knowledge of what sin is when broken, just like lying or stealing. You do not believe God if you think you can continue in known unrepentant sin against God and enter His Kingdom.
The fourth commandment reads: “Remember the Sabbath day to set it apart as holy. For six days you may labor and do all your work, but the seventh day is a Sabbath to the Lord your God; on it you shall not do any work, you, or your son, or your daughter, or your male servant, or your female servant, or your cattle, or the resident foreigner who is in your gates. For in six days the Lord made the heavens and the earth and the sea and all that is in them, and he rested on the seventh day; therefore the Lord blessed the Sabbath day and set it apart as holy." Exodus 20:8-11
The Pharisees criticized Jesus because,
in their opinion, Jesus was violating the Sabbath. Picking grain heads and eating them was a violation of the Sabbath according to the Pharisees, because they took as an iron-clad commandment: "... on it you shall not do any work".
Unlike yourself, I believe God's word in its entirety. I do
not need to rationalize or twist the meaning.