Rav Meir explained today that according to rashi the teacher and barber are considered be'alav imo when they do melacha for you even though you are not paying them since they collect their salary from the city. In the previous lines, we were not paying the guy to give us a drink of water, so why is this a chiddush?
First of all, we see that Rishonim attack Rashi for his peshat and Ramban and others explain that the case is that these workers, since they are collecting their salary from all the inhabitants of the city, they are considered be'alav imo for everyone at all times, even when he is not teaching your son.
The shita suggests that the Ramban's peshat works in the words of Rashi as well.
Another possibility may be not to focus on the money but to say that the worker is not really working for you -- he works for the city and that is the chiddush.