This seems like an absurd interpretation in context. Here's the section, from Matthew, Chapter 5, verses 38-42:
"You have heard that it was said, 'Eye for eye, and tooth for tooth.'[7] But I tell you, Do not resist an evil person. If someone strikes you on the right cheek, turn to him the other also. And if someone wants to sue you and take your tunic, let him have your cloak as well. If someone forces you to go one mile, go with him two miles. Give to the one who asks you, and do not turn away from the one who wants to borrow from you."
It seems like this guy is parsing one phrase ("turn the other cheek") within an inch of its life, while ignoring the context: a series of instructions to be submissive in the face of aggression. If you give your cloak to someone who demands your tunic, how does that say "I won't take such treatment anymore"?
