Stanford and Harvard don't need accreditation because they are among the premiere universities on the planet. Stanford is regionally accredited by the way, I'm not sure why you keep arguing they're not (your confusion is probably that they dropped their ABET accreditation in CS which is not required for CS although some universities do maintain it). Actually, now that I went back and looked it up, even Harvard is accredited, as is every other ranked university I looked up -- Carnegie Mellon is accredited, Georgia Tech is accredited, MIT is accredited.

The two things are entirely independent, you're correct -- but you're making an argument that isn't supportable in comparing the premiere universities on the planet who could, if they wanted, theoretically, eschew the concept of accreditation because they don't need to prove anything about their curriculum with a college that has nothing -- no accreditation, no reputation, nothing at all.