Hi. Safe following distance is the distance required to safely stop at whatever speed you are going. At a typical speed of 90km/hr (that's usually when this "feature" gets engaged - slowing me to 10km/hr under the limit because that's what someone in front of me is doing), the safe stopping distance is around 80-90 meters (perception+braking in good conditions). The shortest follow distance setting I seemed able to find was around double this distance.
tl;dr: I do not find that the adaptive cruise control is engaged at a safe following distance. Indeed, I think it makes me less safe as a driver, because it slows me down arbitrarily without any visual or auditory notification.
So either (a) the car you drove was defective or (b) you are radically misjudging your following distance. I know you are inclined to assume the former, but keep in mind that humans are terrible at judging distances when moving at high speeds, and most people leave way too little space between them and the car in front of them.
(While I haven't driven a Toyota Corolla with adaptive cruise control, I have driven a Subaru Forester, which uses roughly the same following distance; I find it to be a little closer than I'd prefer on my own, but accept it for the convenience and because I assume it can get away with a shorter following distance, since it is not reliant on human reflexes to stop in an emergency.)
Not that this is even a problem in the fist place, I've used dozens of cars with ACC, no Toyota in particular though, and all of them allow adjusting within almost armreach close to a long 5sec gap. Put closer distance in heavy traffic to prevent lane jumping in front of you and 5 sec for comfortable highway cruising.