A long discussion is probably better off in a science forum.
However, yes, a truly altruistic species (that is, a species in which the individuals make sacrifices for others with no survival benefits for the genes that induce altruism) would be impossible.
However, when biologists speak of "altruism", they are referring to the behavior that is seen in social or eusocial species (or symbiotic behavior between different species) where "sacrifices" made by an individual actually does lead to an increase in the genes or alleles that induce the behavior.
I'm sure the show explains how this is possible.
Here is a link to a relatively recent thread on how behavior that is seemingly counter to reproductive fitness
can nonetheless be favored by natural selection -- it did focus mainly on homosexual behavior, but the principles are similar.