RWU - Yes, it certainly did. I approved of that system, and certainly trusted my colleagues to make good decisions - which is the necessary requirement for that system to work.
It might also be relevant to add that we would always(pre-start) discuss my intentions for the "grey area" take off decisions, such as various overheat indications. I don't want to get type-specific (because the original question was re: Boeing) but for one particular failure indication, I had a different policy from most other people, so I made sure that if it occurred before V1, I wanted an "Abort" call.