The debate between Jesus and the Pharisees about plucking and eating corn did not concern labour on the Sabbath but concerned eating food which was allowed only to priests.
When Jesus is asked to justify allowing his disciples to pluck and eat corn on a Sabbath, he appears to reply with an irrelevant story. If we assume that the Pharisees are complaining about the disciples performing labour on a Sabbath, it is irrelevant to answer them with the story about David feeding his men on the Bread of the Presence, because this story does not relate to performing any labour. Another problem lies in the fact that there are no rabbinic traditions which forbid performing the labour of preparing a handful of food on a Sabbath, and there are specific rulings which permit this amount of labour (though no more). These difficulties are eased in Matthew and Mark who append other comments by Jesus which appear to be more relevant, but this still leaves the problem that Jesus’ first reply appears to ignore the issue at hand.
A comparison of some old traditions within rabbinic legal collections indicates that the real issue was not Sabbath labour, but eating untithed food. Tithing could not be performed on a Sabbath, so freshly harvested food still contained the Heave Offering which only priests were allowed to eat. If this is the case, the story of David allowing his men to eat food only permitted to priests, would be an appropriate and irrefutable reply.