i don't really think that this is true at all. what you'll do is either be more careful and avoid the situations to begin with (like not riding to the right of cars at intersections, etc), or, like you did, either turn quickly/maneuver, or, *gasp*, stop very quickly using various skidding/skipping techniques. it can absolutely be done. people seem to think that their front brakes are going to stop them ever so much faster than certainly properly executed brakeless techniques. that's just patently false when it comes down to it in most real-life traffic situations. from what i've experienced, and what i read about on these forums, most collisions (especially those where the rider wasn't just being careless) are not going to be avoided by an extra foot or two of stopping distance.

that said, i think you should definitely ride with a brake if you are a rider who doesn't pay very close attention to all of their surroundings or who rides like an idiot (this is to be meaningfully distinguished from riding like a maniac -- which can be done, albeit assholishly, fairly safely and skillfully). i'm not at all saying that you are such a person, but i think a lot of people think that a front brake is actually some sort of necessary, "safe my ass," emergency tool.