The way I understand it is that it doesn’t really matter what you do, whether other people see you, or even what they think if they see you doing something. It’s only how you perceive the situation that causes embarrassment. For example, two people could do the exact same thing, and get the same reaction from people who are watching, and it’s possible that one feels embarrassed and the other one doesn’t. Understanding that in most situations, like what @marinelife said, “everyone else” is less focused on a particular person, and adding how little most people probably care about general strangers, there is no need to feel embarrassed.
I would slightly reword the phrase to say “you have the choice to not be embarrassed”.
The difficulty lies in the practice of letting go of the fear, anxiety, worry, and perceived expectations of others (and yourself) that you identify as part of who you are which cause the feeling of embarrassment; so that you can choose to not be embarrassed. Like many personal growth efforts, it’s simple, but not easy.