It really is true that most schools no official cut offs. However, GPA and GRE are the easiest comparable data sets. Every competitive program needs to weed 30-50%, or more, of the applications; this is natural, as, aside from a few "for sure admit" starts of each round, a lot of applicants are going to fall into the "strong middle" category, and it requires effort, ratings, discussion, the works, to figure out which strong applicants to reject.
This means that, whether it's one poor junior prof., or each member individually, there has to be a weed out phase. In a way, it does not matter if there is a rule: "GPAs under 3.5, GREs under 1250 combined" or if it is ad hoc: the result is about the same.
Put yourself in the committee member's shoes, and you can see how it works. You have a pile of fresh applications no one has seen. They have either been sorted by sub-category (eg., in political science: theory applicants, IR applicants, etc.), or they have not. Either way, what does Junior Professor Smiley do with each app? The same thing: first he checks: a)what school the applicant went to b)GPA and GRE c)does he know any of the letter of reference writer's or recognize any names at least. Immediately all of the above info results in the frame of mind decision:
the applicant looks a)very strong b)strong (here, which school you went to is crucial...'He went you Yale'=he is certainly not DUMB) c)the scores are a bit low, and the school ain't so great d)the scores are too low, and the school ain't so great.
Then he has to weed. He will weed all the D)s. He will then likely weed half of the C)s.
If everything looks in order EXCEPT one main date-point, he checks: school pedigree.
In all cases where he can't easily arrive at a c or d, he reads the statement of purpose. In the cases where he is almost sure it is a c or d (weed or weed with great prejudice), he reads the statement of purpose QUICKLY.
If you are in the A) or "frame", he reads your application in its entirety CAREFULLY. If you are a C) or D), he reads everything as well, but he does so QUICKLY.
At the end of reading EVERY App in its entirety (or for some schools, only the A)s and B)s and some C)s ), he assigns a numerical value. The ranking system and breakdown varies. According to a paper published in a political science journal on the "Science of Political Science Admissions" in 1995, Harvard Government would rank out of 14. Why 14? Because 1/14 is about 7%, and that is also the average acceptance rate. In other words, you better get 11-14 to make it to serious final round debates in full committee.
How about the final rounds? For the low GPA/GRE folks: you better have an incredible reason to have gotten this far!!
How does the final round work? That's not clear. Certainly there are a small handful of students who just knocked the socks off everyone who read their app. They are in. That is maybe 1/4 to 1/5 of the spots. The rest are haggled over. Either you appeal to a few profs, or one prof in your area maybe just loves you, and fights for you.
And the rest, as they say, is history.