I never applied to these places, so take this with a grain of salt. But when I was recruited by Google several years ago, the recruiter was enthusiastic but got

I never applied to these places, so take this with a grain of salt. But when I was recruited by Google several years ago, the recruiter was enthusiastic but got back to me several days later saying that she simply could not sell the hiring manager on me because of lack of degree. In LinkedIn's case, they mistook me for a recent grad due to creating a new profile on their website, and after setting up an initial phone call that revealed this error, I never heard back from them (truthfully, the latter opportunity was probably not what I'd want anyway). You're right that I'm lacking in some skills, but it seems like the skill bar is set much higher for a person without a degree. You have to be truly exceptional to warrant consideration.