I think there are at least two different answers to that question, based on there having been at least two different groups of supporters of AAPs. One group thought you could actually have non-quota AA. This group was naive. The other group didn't for a minute believe you could have non-quota AA, but cynically paid lip-service to that goal.
What I know best is higher ed. In higher ed in New York City, the wedge issue was remediation. AA supporters insisted you could take the most rigorous undergraduate college in America, the City College of New York, and relax admissions requirements for students who were allegedly just shy of meeting the school's Olympian standards. The AA students were admitted in 1965. But they weren't close to meeting CCNY's admissions standards; they weren't in the same galaxy. In case you think I'm exaggerating, the book Errors & Expectations by Mina Shaughnessy, who ran the CCNY remedial writing program at the time, contains hundreds of examples. (The book is out of print, but I bought it used from half.com.)
In 1969, some of those same students took over buldings at CCNY, demanding that all admissions standards be eliminated; the City University of New York trustees caved in, and the following year made all of CUNY an "open admissions" system. And the CUNY degree -- particularly CCNY's -- was soon worthless.
During the 1990s, I taught remediation at CUNY for several years. While the media spoke of CUNY's remedial classes as functioning on a high school level, some of my college-level students cut to the chase: the remedial classes functioned on a third-grade level. (Note that the students I cited did not attend one of CUNY's "big three" of Baruch, Queens, and Brooklyn colleges, where standards were presumably higher.) And remedial classes were dragging down the standards in "college-level" classes, as remedial students were permitted simultaneously to take remedial and college-level classes.
Under AA, all over America elite universities began routinely accepting students who could not possibly meet their academic standards. And so began the regime of "mismatching," and a vicious circle of black failure that has since spread like ripples from a stone, to graduate schools and to predominantly black public schools.