Hell no.
People can also pretend to take offence or be overly sensitive or just plain wrong. People like this are not to be humoured.
An example is that a few years ago and on another forum one poster was all offended about me using the term "neurotic" to describe the test subject to Sigmund Freud's work. (I said they were a "very small group of middle class neurotic Jewish women") She got heartily offended and tried to get the forum to see how offensive and bigoted I was. I pointed out firmly that the women suffered from Neurosis (such as Anxiety Disorders and Depression). Therefore the group of women were Neurotic in the clinical sense of the word.
Ought I have apologised at her not understanding? Ought I have had to own her misunderstanding?
So NO this video is just plain wrong.
BUT there are definitely instances where you are in the wrong, and in these instances were you know and they know, and you need to to be an adult. In these instances you need to give unconditional apologies.
You seem to be lost in your own thoughts.