Why Is A Degree So Important, If the Employer Couldn't Tell?

This NYT article tells the story of a high-profile MIT Dean of Admissions who resigned because she had claimed she had college degrees when she in fact had not even a BS degree. She had worked her way up into her present position over the course of 28 years at M.IT., and apparently was extremely well-respected and liked at M.I.T. and elsewhere (she recently published a book on admissions). While it is hard to condone her gross resume padding, lost in the discussion seems to be the fact that her employer couldn't distinguish, objectively, that she lacked a college degree. It does beg the question, just a little bit--is it dumb for employers to treat a degree as the sina qua non of generic credentialing for knowledge workers? Shouldn't a degree be a "plus", one of many things that employers weigh when deciding to hire someone? And once hired--does it matter at all?

From a strategic-HR perspective, I have thought that it would be really smart to be open to non-degreed people. You would of course have to have a good, rigorous hiring process, rather than relying on the crutch of assessing their degree and grades, but if done right, you would be able to exploit a niche and attract good people for, say, the lower half of the market rate. And they would also be much more likely to stick around, since you would be one of few employers who would give them a shot even though they lack that precious college degree.