I've had a good deal of experience with Geniuses. Generally I divide them in two categories: those that love the Apple brand and do what it takes (within reason) to get you going, and those who are either arrogant corporate wannabes who get their jollies telling customers "no" or are too "smart" to do further research. Generally when I get the latter I either ask for a manager or politely say "OK," and then make an another appt. at another store w/ a different Genius. It really just depends on whether I'm in a fighting mood or not. As always, the squeaky wheel gets the oil.
As to the spots, it is possible to get splotches by pressing on the screen, but you'd have to press hard and for a minute or two. It can also happen if a flying blunt object hits the screen or you subject your screen to sub-freezing temps for too long. I'm guessing none of that is the case here. More likely is that you have a defective screen. I recall the final PowerBook model was famous for having milky white spots which Apple did not want to take responsibility for until the issue was pervasive and creating bad publicity. Is that is what you are seeing?
My advice is to either go to another Apple Store (get the manager involved if you have to) or call up. Generally I don't like to call b/c I always get the feeling they are paid by the number of people they don't have to refer to a 2nd line tech, but in this case it may be the solution to your problem. Since the issue requires someone to look at your machine it will go to the depot and more than likely they won't ask further questions, but rather just put a new screen in.
In any event I wouldn't let them bully you around. There are good, helpful Apple tech people that genuinely want to make things right. The frustrating part is that you have to discover them though a "hit and miss" process.