Glover, for instance, writes that
All disabilities involve functional limitation. This contrasts with purely socially constructed disadvantages - for instance, those facing members of ethnic minorities in a racist society. […] In theory, social output is not in the same way essential for something to be a disability. Robinson Crusoe, alone on his island and unable to walk properly after a stroke, would still be disabled.What pisses me off about such examples is that they wrongly suggest that they illustrate a normatively relevant distinction. This is not the case. I'm not just complaining that disadvantage derives, in most cases, from the combined effect of social discrimination and functional impairment, which Glover would not deny. I complain because the use of this example suggests that we can make a distinction that in reality we cannot make.
The example wrongly suggests that we can use a "Robinson Crusoe" test as the litmus test for distinguishing authentic disabilities from cases of purely socially constructed disadvantage. Take the example of deafness. According to the "Robinson Crusoe-test" deafness is an authentic disability: "Robinson Crusoe, alone on his island and unable to hear properly after a stroke, would still be disabled." Sound enough, but so what? The reason why a deaf Robinson Crusoe is disabled is that he lives in a very special social environment, an environment in which he cannot cooperate with other human beings. It would just be wrong to infer that, since deafness is an impairment to human flourishing in the Robinson Crusoe environment, then the disadvantages to which it leads in other environments are purely socially constructed.
Consider this example: having a white skin is an authentic disability in many natural environments. "Robinson Crusoe, alone on his island, without clothes, with his melanin-poor white skin, would still be disabled." (The relevant comparison, here, is with a black-skin Robinson Crusoe, who would be able to stay under the sun for longer time without burning is skin.) Now imagine a society, in cold climate, where black people are more powerful than white and black people treat white just like blacks were treated by whites in nineteen century America. Should we conclude that the disadvantage attached in this society to being white is not purely socially constructed, just because whiteness counts as a disability in the Robinson Crusoe case?
More generally, it is not at al obvious at all that the Robinson Crusoe case is relevant to judge whether something is a disability or a "purely socially constructed disadvantage", because in most cases there is no useful parallelism between this case and the cases in which people live in a society.