But private institutions can defy the Constitution all they want, right?
It depends what the issue is. Take the First Amendment, for example: if a private company wants to restrict speech, that's their right. What authority, under the Constitution does Congress have to say a small diner can't have separate seating for whites and blacks? In my opinion, they don't. Does that mean I think diners should be able to segregate seating? Absolutely not.
The SCOTUS unanimously disagreed with you. Remember this as you enter 1L.
http://en.wikipedia.org/wiki/Heart_of_Atlanta_Motel_v._United_States
I spent 30 minutes trying to remember that case.
And like I said, I realize that the Court disagrees with me. And if I were ever in a judicial position, I'd put my personal beliefs aside and go along with the precedent. I think the Court got the case wrong, but at this point, we're too far along to reverse years of precedent.
If you take a look at the actual opinions, it is entirely possible that future court could invalidate Title II of the Civil Rights Act of 1964 without straining the concept of precedent. The majority opinion by Clark based upholding it on both the Commerce Clause and the Congressional findings that discrimination against negroes led to a considerable interference in interstate commerce. If a future court found that permitting businesses to discriminate would no longer lead to considerable interference because it would no longer be a widespread practice, then it would be conceivable that Title II could be struck by a future court.
Note: Black's concurrence asserted that the Commerce Clause by itself without needing a finding of interference caused by discrimination was sufficient to uphold. Douglas and Black in their concurrences asserted that Title II could be upheld on Fourteenth Amendment grounds as well.