No, this isn’t true at all. My teenager has never been punished once in his life, and he’s turning into an excellent human: hard-working, compassionate with self and others, honest.
I would define punishment as “intentional infliction of suffering for purposes of behavior modification.” As stated, that’s flatly unethical, especially with your own family.
Now, he experiences consequences of his actions all the time. Scratch the counter-top? Win an afternoon of helping me refinish it. That works because it’s directly connected to his actions, and because I treat it as a learning opportunity rather than yelling at him or banishing him.
There are more possibilities than “punishment or permissiveness.” Kids need structure and to understand and experience age-appropriate consequences for their actions. But that doesn’t mean they need arbitrary suffering imposed by people they’re supposed to love.