Not at all. The case is where the teacher can work and wants to work. In the context of the story, his statement expands to, "If I can't work, I won't eat." It's about his right to participate fully in the community.

Zen also has a long tradition of mendicants monks. E.g.: https://tricycle.org/magazine/zen-and-art-begging/

The Buddha himself spent time living as a beggar: https://en.wikipedia.org/wiki/Gautama_Buddha#Renunciation_an...

And of course there's a long tradition of charity and caring in Zen that runs to this day. For example, San Francisco's Zen Hospice: https://www.zenhospice.org/about/our-values

From each according to their abilities, to each according to their needs

As he got older and was less able to work his ability would diminish and his need would remain static.

So his pupils would need to work to feed him, but he showed willing to do what little he could, thus fulfilling a social contract / fairness need.

Proper teaching and especially mentoring is hard work. So if they do not work, then they are not a teacher, right?

Remember that Zen likes to confuse people with logic to achieve better understanding.

(It also attacks defining people by their occupation a few times.)