It's true that the value of the speed of light depends on units that are relevant to humans. To suggest that this implies something about physics is absurd. Physics is in fact independent of the actual value of the speed of light.
The idea that the speed of light in vacuum is constant in all reference frames is a postulate of special relativity. Both special relativity and general relativity are confirmed by numerous experiments.
Edit: Note this is also a TEDx talk, not regular TED.