The "dirty secret" of Crossfit is that they don't do much to actively ensure the quality of local affiliates, and therefore the brand doesn't always mean much. My personal experiences have all been great, and my coaches have always been extremely safety-conscious, but in light of the nasty things I read on the internet, I wouldn't encourage anyone to blindly trust whatever local Crossfit affiliate happens to pop up down the block. Rather than thinking of Crossfit as a guarantee of a certain standard of quality, think of it as an approach to fitness that is interpreted in various ways by coaches of varying competence.
Also keep in mind that the coach can't always see when you need to ease up or stop. Sometimes they can, but they can only see what is apparent on the outside; they can't feel what you feel.