Short Answer: No, the analogy doesn't hold up well.
The analogy would be astute if and only if interests among people were random- they aren't.
Human beings have universal needs along several axes- physical, emotional, arguably spiritual.
This leads me to conclude that in a hypothetical space of all possible interest $s$, there could be defined some directed function $f$ to describe all practical human interest space, and that this function would have some $x$-dimensional vector tendency within space $s$ and therefore human interests would co-vary along those vector tendencies.
It would also follow that any interest pursued according to those vector tendencies would correlate with other human interests-
In effect, self-interested but human interests correlate with altruistic but human interests in the hypothetical geometric space of all possible interests. That is, the controlling property is the humanness of the interest.
The random variables you mention in the space of all possible covariances have no identifiable similar $x$-dimensional vector tendency, certainly not to the same degree.
I have no doubt that a philosophical answer would look very different indeed.