I agree with you - the best route is probably to stay with accredited institutions. Unfortunately they can lose their accreditation at some future point and then Google searches will produce only "LOST (or NO) ACCREDITATION" type of results. The context of whether or not the school was, at one time, a valid vehicle to education will be completely lost.
I feel this is what has happened to Kennedy-Western. At one time John Bear lists Kennedy-Western in the top 100 distance learning schools and within a decade changes his mind. Now Google searches produce DIPLOMA MILL results with no context as to why anyone would ever have wanted to enroll in such a place. Potential employers will likely conclude that Kennedy-Western graduates are not "educated"; an unfair assessment.