Nothing "guarantees" availability", but belonging to the free program for a particular rental car company (Avis Preferred, Hertz Gold, etc), and being logged in to that program when you make the reservation, greatly increases the likelihood of availability, as (at least with those two programs) they have to put those cars on a display board that everyone sees, so they don't want to put "no car available" on that board, while people who don't belong to the rental car company program are told in private if there's no car available. And thus if they don't have enough cars for everyone, they're more likely to want to tell that to people in private. So even if for that reason alone (and that may not be the only reason), your odds of getting a car of some sort are greater if you belong to the rental car company program. And in case the car you get isn't the one you want, you are at the booth for the program members near where the rental cars are, instead of the main reservation booth back inside the airport, and the booth for program members is much more likely to be able to accommodate you than the booth back inside airport that non-members have to use.

So were your friends and family (who you said had experiences with no cars available) members of the rental car program and going to the display board to find their cars? Or were they non-members going to the main booth inside the airport, as most people are?