The priest in the OP is right. It is not explicit in the readings but implied. It is about the precepts of the Church, the absolute minimum each of us must do in order to be saved.
In the Gospel reading for 10/6/2013, Jesus is speaking specifically to the 12 Apostles.
**"Who among you would say to your servant
who has just come in from plowing or tending sheep in the field,
'Come here immediately and take your place at table'?
Would he not rather say to him,
'Prepare something for me to eat.
Put on your apron and wait on me while I eat and drink.
You may eat and drink when I am finished'?
Is he grateful to that servant because he did what was commanded?
So should it be with you.
When you have done all you have been commanded,
say, 'We are unprofitable servants;
we have done what we were obliged to do.'"*
Though Jesus was God, he became like a servant. Jesus came to serve and not be served. The Apostles were to do the same, to serve the faithful and not be served by the faithful. Jesus tells the Apostles that they must do more than just the minimum. This lesson is applicable to the successors to the Apostles, the bishops today, and by extension the priests and deacons who receive their faculties from the bishop and have power to administer the sacraments only because of the existence of the Bishop. If all the priests and bishops and deacons do is say Mass and sit in the confessional one hour per week, they are doing the absolute minimum and are unprofitable servants.
The parable is about the leadership of the Church through the Apostles and their successors. It is about saying Mass, administering the sacraments and the salvation of souls as servants, not as exalted leaders. The main way that the shepherds lead us to salvation is through the Mass and the Eucharist. But that is just the beginning. They are to do more because saying Mass is their absolute minimum requirement.
We are to do more as well. The precepts of the Church tell us the minimum we must do in order to be saved - Go to Mass every Sunday and days of obligation, go to confession once each year, receive the Eucharist once per year, abstain on Friday, etc. If this is all we do however, we have done the absolute minimum.