I wholeheartedly agree that people often have poor self reflection skills, which can mess up any personality assessment.
Also the frame of reference can affect the outcome a lot. When I was tested for DISC, I was told that I should answer as "the work me" and not think about how I would behave at home or with friends. When I was given the Myers-Briggs test, I was told the opposite: to completely forget about how I do things at work, or what I'm able to do if the situation calls for it, and only answer based on my personal preferences. As a result, my DISC profile is so different from my Myers-Briggs type that you wouldn't guess that's the same person.
However, the questions that the guy on the video was referring to didn't sound like the actual Myers-Briggs test questions. I'm not saying that the official test is immune to people not really knowing themselves or answering in an aspirational way (although what you aspire to be can also say something about your personality), but at least there is a huge amount of data behind it to help calibrate the answers. If, for instance, what the guy on the video says is true and most people think of themselves as introverts, there is statistical data there to determine the level of introversion compared to other people.
The MBTI is not perfect, but it's not as bad as that.