I know of a good number of high-end steakhouses that require every steak to be checked with a thermometer in order to guarantee doneness. If you are preparing a steak that costs you $10-15 to bring it in, are you going to trust touch alone, and then be giving away free steaks and other comps if the grill cook is having an off night? Its your own risk. Ive worked the grill at many places, and have rarely missed on what the customer expected, and I do it by touch. I also dont use a thermometer when Im preparing pork butt or brisket, I let the meat tell me when its done. And whenever I work somewhere that does a lot of steaks, I also set up my grill to be hotter at one end and gradually cooler towards the other. So if I have a table that has a medium rare steak and a well done steak, I put both steaks on at the same time and they come off at the same time. I dont have steaks waiting to go on or out. So how can anyone tell me how long to cook their steak?
But I think the original question is what do the general public know, and that is most people know what they want it to look like and the terms used to describe it. The average person rarely knows the thermometer temp of how they want their steaks. And really the server should have just been able to ask how they would like the steak prepared and not worried about the semantics of doneness or temperature or bothering the chef to see how to do her/his job. Then that lets the customer decide how to answer the question (Medium, 160, or bloody as hell).
(been cooking since I was 28. Of course you dont know if Im 30 or 65, so that doesnt really tell you that much about my experience...)