You sound like you work for a company I would choose to avoid. I say this with 12 years of professional experience under my belt and a BS. If you arbitrarily cut off people without a BS, you are missing some of the cream of the crop, particularly those students coming from a homeschool or alternative schooling background. If your company allows you to categorically screen people as you claim to, I would avoid working there.
Of course, personally I think you are full of shit. Anybody looking for programmers these days is going to take a long, hard look at anyone that seems competent, regardless of academic background. Programmers are hard to find, and nobody I know screens for college degrees over experience. That's just dumb.