Or at least, they are not sending the signals they think they are sending.
The signalling theory was introduced by Spence in his 1973 paper Job Market Signaling.
His basic idea is to view the employer as buying a lottery ticket when he hires an employee. He knows extremely little about the attributes of the potential employee that he is really interested in and thus has to draw inferences from easily observable attributes such as "education, previous work, race, sex, criminal and service records, and a host of other data".
Many of these attributes cannot be modified (e.g. race and sex) but those that can be modified and especially those where the cost of improving the attribute is low compared to its impact on the employer can be manipulated by the prospective employee to signal the employer about his qualities.
Spence primarily views education as a signal for work potential but he readily admits that it might, e.g. be rather used as a signal for status instead. However, the important point is that "signaling costs are negatively correlated with productivity" (or with whatever other property you want to signal your potential employer about).
Someone who has a high work potential will be more willing to get an education because getting an education will be cheaper for him than for other people - not just in terms of money (although you could argue that scholarships, a lower chance of not successfully completing the degree, ... can make it cheaper in terms of money) but also in terms of "psychic and other costs", e.g. time. Someone who already has a high social status will find it easier (i.e. cheaper) to get an ivy league education to signal this status to his employer than someone who intends to get that education solely to mislead employers about his true social status.
Although different signals can be appropriate for different types of work, the signalling value of getting an education is not about the content about that education. You aren't primarily demonstrating that you learned any useful skills. In fact the signaling value of an otherwise completely useless education might be even higher than that of an education that has a very reliable return in terms of real-world applicable skills, e.g. most mathematicians are not hired because they need theoretical math skills for their job but because mathematics has a reputation for being insanely hard. For the vast majority of people it doesn't make sense to study mathematics because the cost would be far too high and the rl skills learned are low. The same goes for almost any PhD degree - the knowledge learned while earning the degree is way too specialized to be of any use to your employer - but the fact that the cost of getting a PhD was so low to you (because you are so awesome) that you felt it economically worthwhile to get one anyways is a strong signal to any prospective employer.
That's the way those who think that signals are important (there are other theories that explain the value of education in terms of accumulation of human capital) think that signals do work. And correspondingly these are the signals they think they are sending by getting an education. Now, how do you disagree?