Of course it is, but how does one come away from that video imagining its authors simply missed that most basic fact (among others) ?
Clearly, the film's starting point is that as pilots we KNOW that Density Altitude can kill; likewise a heavy load, a tail-wind, an up-slope and, to be sure, a draggy, clingy surface. (Before we even get to our own skill level and our own aeroplane's declining vigour.)
The point of the Air Safety Institute video (far beyond just preaching "caution") is that, added to all that, your POH can also kill, if you put unwarranted faith in its P-chart claims.
The experiments that the video team took pains to do turned up the shocking results that book take-off figures were, in the real world, fully 30% "optimistic" (in 2 common GA types).
Yes, of course, they did these experiments on bitumen but the whole point of P-charts/Tables or Take-Off Calculator apps is that a good set of numbers from any given situation can (by extrapolation/interpolation and known factors) yield rough results for most others. With, of course, an added margin for safety.
But that unaccounted-for 30% error stretches 'rough' to its very limits - and in quite the wrong direction.
Which is probably why AOPA/ASI recommends adding 50% to book figures and urges us to "Go fly and test this for yourself!"