Edit: Those who are low in skill benefit more from college than those who are high in skill because there is a saturation point (if this were false we would all attend college multiple times). If "elite" firms are looking for the "elite" people who were already at the saturation point before coming to college, then for the population they want it is probably true that attribute (skill+intelligence) causes signal (degree).
Employers who do not need to hire the most "elite" employees need not behave this way.
As an aside - i don't think this is college specific. I think all signals - indeed, all causal lines - follow the format you just laid out. Suppose you wanted to Signal an Attribute. People will treat your signal as evidence for the attribute if they believe one of the following things:
Attribute influences Signal (preexisting skills enable college education, health enables large peacock feathers)
Signal influence Attribute - (college education increases skill, muscles cause strength)
Hidden factor influences Signal and Attribute. (intelligence enables both college education and skill acquisition, hormones increase both secondary sex characteristics and fertility)
I can't think of any other Signal-Attribute configuration.
It's a well-known fact that college graduates make more money than high school graduates who do not go to college, but the reason is not clear. Bryan Caplan offers a typology where he splits the gap between the income of college graduates and of high school graduates into three parts: human capital, ability bias, and signaling. Caplan also warns economists of education against conflating ability bias with signaling. The (human capital + signaling) total gives the "return on education" for a college degree -- the part that is causally due to getting a college degree. The (human capital) part alone gives the return on education through the channel of improved productivity, whereas the (signaling) part gives the return on education through the channel of being able to convince potential employers that they have higher productivity. The (ability bias) part can be thought of as selection bias for pre-existing ability: people who go on to graduate from college differ from people who do not go to college in terms of their pre-existing abilities (here "pre-existing" does not mean "innate" -- but rather it means what they had before starting college, or what they would have acquired through natural maturing even if they hadn't gone to college) and these people would likely have earned more (compared to the ones who didn't go to college) even if they had chosen not to go to college.
I want to look at the signaling channel more closely. A college degree does send a signal of some sort to potential employers, and stories of college dropouts who achieve great success notwithstanding, many employers, particularly for high-skilled occupations, prefer workers with college degrees even if the degree is not directly related to the work on the job. But why, precisely, does the employer value the degree more? I can categorize the possible explanations into three categories:
What do you think is the breakdown of signaling between (1), (2), and (3)? Any other thoughts about whether the question is well-conceived, and about alternative formulations of the question?
UPDATE: Lauren Rivera's article on how elite firms hire, which was discussed by Bryan Caplan in an EconLog blog post, is relevant.