It was just assumed that if your parents were above the "means" they would help out any way they could because that's what was expected of them as parents.
College was also seen as an enabler and not an expectation for my generation.
Or...if your parents spent all the college fund sending your sister to UCLA you could join the army and emerge as an "adult" so your parents' income wasn't taken into account and get grants and loans on top of the G.I. Bill.
I don't think my parents could've afforded to send my sister to Stanford back then which is roughly the equivalent to your average state school today (completely guessing here). They probably would've found a way though.
My point still stands though, means testing was intended to get the best and brightest into college even if they're poor, couldn't even imagine Reagan/Bush entertaining the idea of giving middle-class kids a free ride -- in fact I can even picture Reagan on the TV saying "Uncle Sam ain't your baby daddy!"
Note that the UK does exactly this, last I checked.
The US already does this for federal loans, though it's not the default option, and the servicer (Navient) has been accused of actively steering borrowers away from the option, because it hurts the value of the loan-backed securities that Navient sells.