You shouldn't and wouldn't rely unfailingly on what other cars merely report. If the car in front of you insists its maintaining speed while your own readings indicate its slamming on its brakes, you should assume it's slamming on its brakes.
However, if the car three cars in front of you just broadcast "I'm doing an emergency stop right now", that's really valuable data. The human in your car won't know anything is wrong for at least a second. The human driver behind you would know about it before the human driver in front of you.
That will be the most common failure mode for computer-driven cars: how easy they are to bring to a stop. (And, yes, that's probably criminal behavior.)
A computer-driven car, though, wouldn't (shouldn't) just immediately slam on the brakes because of that signal. It would tighten seat belts and start slowing down, but it also would want to avoid getting rammed by the car behind it. It can make very accurate estimates about its stopping distance and use all of it.
However, if the car three cars in front of you just broadcast "I'm doing an emergency stop right now", that's really valuable data. The human in your car won't know anything is wrong for at least a second. The human driver behind you would know about it before the human driver in front of you.