OK, first of all I want to say I really dislike the videos that this guy puts out, since he is promoting unsafe handling of chemicals. He might know what he's doing, but it's a terrible example.
To the actual question: surprisingly there are nearly no sources on this. I can understand that this isn't something a lot of people would try nowadays, but I imagined that a lot of people tried 50 years ago or something like that.
There's one science article describing a blind taste test of three persons in comparison to distilled water, and they couldn't spot a difference.
Another paper describes a difference, and also cites older research that showed that rats avoid $\ce{D2O}$ if they have the option to choose. But that might also be smell. It is known that deuterated substances can have a different smell and taste.
Heavy water also has a higher density and viscosity, so that might also be a factor which makes it "taste" different. Fun fact: it also has a different color.
And well, he didn't do the testing in a scientific manner, which would at a minimum include a double-blind format.