Paul Watzlawick said that. He is one of my favorite authors. When I was 14, I read his book, “How Real Is Real?” It changed my life and thoughts on communication.
Everything you do broadcasts YOU to others. There is no way to not be you, therefore, it is impossible to not broadcast yourself.
Even when you avoid communicating or avoid trying to behave a certain way, that is still communicating through your avoidance, body language, choices of ‘change of topics’ and so on.
Even not communicating is a communication. Ghosting is a great example of this (It’s communicating that you’re an asshole. LOL!).
So, once you realize that everything you do communicates whether you want it to or not (and maybe the message you send is not one you want to send), then perhaps the priority shifts to communicating effectively what you desire to communicate about yourself.