The guy in the video has gotten some specifics scrambled up, as you might expect for someone outside the field. However, let's focus not on the details but on the big points.
1. Some physical variables (e.g. the cosmological constant) which could have a whole range of values, so far as we know, have values within the extraordinarily narrow ranges which would allow for complex chemistry and thus life.
2. The standard scientific explanation, involving a large or infinite ensemble of universes, and nobody picking arguments in the dead universes, is only made up to avoid religion.
Point (1) is correct.
Point (2) is incorrect.
There are several strong, independent, prior reasons for suspecting huge ensembles of parallel universes.
In quantum mechanics, the time-dependence equations, confirmed to great accuracy, have the simple property of being exactly linear. Unless that linearity breaks down on some as yet unmeasured scale, all of the possible outcomes allowed by quantum mechanics must actually occur in the abstract quantum-mechanical space.
In trying to solve for the dynamics of cosmology, involving the still partial theory of quantum gravity, one finds solutions such as an inflating space giving birth to an infinite number of non-inflating universes. Other solutions also involve infinite numbers of universes, all within the manifold of which our space-time is one component.
Whether the quantum parallel 'many worlds' exist is indeed a very hard thing to test. Opinions differ on whether they obviously exist, as our equations imply, or obviously don't exist since they boggle the mind.
Cosmological behavior is partially testable. A number of cosmologies have already been discarded in the light of experimental data. So it's quite possible that data will soon steer us toward a cosmological picture which either does or doesn't have many universes in the full manifold.
Here are two good resources to follow up on this:
Lenny Susskind's book "The Cosmic Landscape"
Max Tegmark's May 2003 article "Parallel Universes" in Scientific American.
Tegmark gets a bit far-fetched at points, but is still fun.
(published on 01/13/2011)