Is the degree someone earned really that private? What would happen if...

I have have only been asked to sign a document once to prove my education, and that was for Sun Microsystems back in the 90s. Every other employer has taken my word for it.

I can see how the Yahoo issue happens - you get this guy who has held some big positions, and really you are hiring him for his background, not his BA. You confirm that he was at PayPal, for example. You don’t worry about the rest.