In my opinion the dealer doesn't know what he is talking about. Your description of the problem indicates a fuel problem. Clean the carb real good and as I said before install a new float needle. Part number 394681 if you have a gravity feel system or part number 394683 if you have a fuel pump. Also clean the fuel lines and make sure there is nothing in the tank, which might be plugging the fuel outlet. This manual might also help out.
http://dl.dropbox.com/u/12502267/B&S Service Manuals/01_270962SingleCylinderLHead.pdf
http://dl.dropbox.com/u/12502267/B&S Service Manuals/01_270962SingleCylinderLHead.pdf