Indeed. The scientific idea of isolating variables is usually impossible in the social sciences. Coincidentally, this was one of the reasons I became fed up with economics my freshman year and finally transferred into physics; I couldn't stand the insistence by economics professors that what they did was on par with a science.
I apologize for not having any concrete research to site, but this question interested me so I'll go ahead and write a few thoughts on it:
It's still a little unclear to me the context within which Spencer puts "survival of the fittest." The guy in the video makes it sound as though the theory claims that the relationship between being "fit" and "success" is environment independent. If that is indeed the case, it's certainly flawed. If I put a population of monkeys of monkeys in the desert and another in the rainforest, the resulting survival of the populations is clearly not an indicator of the fitness of the monkeys that I put in the desert vs. the ones in the rainforest. It's mostly a comparison of the effects of the two different environments on monkeys.
The alternative is that he's claiming that the when the social system itself was set up, the most "fit" ended up at the top of the pecking order. This also has an environment flaw in that it doesn't take into account the fact that some may have been, by chance, in a better position to exploit the system, a system which allowed them to stay near the top without competition from those lower on the rungs or "in the desert," so to speak. In addition, even if we granted him that the system was set up in such a way that it organized levels by fitness, it doesn't account for inheritance of said positions. The advantage of someone born of the upper-class vs. the ghetto is an environmental one, not intrinsic fitness.
Finally, it defines fitness in a way that is rather contrary to the usual Darwinian one. When we're talking about other animals, fitness means ability to catch prey, escape from predators, attract mates, even be clever. These are all based on intrinsic physical properties, and generally the desires a population are the same. All the animals are trying to eat and reproduce. In the social context, desire has to be made into a measure of fitness. For instance, I'm a physics major, I'm not sure exactly what I'll end up doing when I graduate, but I can almost guarantee that I'll make less than my friend who's going into Investment Banking. Does this mean that he's smarter than I am? Is he going to have an easy time finding enough food to survive while I struggle to make it on crackers and toilet water? No, of course not. It simply means that he, for whatever reason, had a desire to go into finance, while I opted for a more intellectual pursuit. Now, in some ways, perhaps he is more "fit" than I am, but the video implied that Spencer would say that because I won't make as much money or have as much social influence, I must be less intelligent and fit.
: I think you could argue that there is *some* kind of "survival of the fittest" mechanism in human society, but you would have to alter basic evolutionary theory to include a number of outside and non-biological inheritance factors, as well as redefine the common biological meaning of "fitness." At this point it's almost a blatant misrepresentation to even use the term "Darwinism."