No. There are tons of different options. Check out some of the menus on allears.net to get an idea.
We love the BBQ ribs at Flame Tree in AK and the fish and chips at Columbia Harbour House in MK. There are plenty of deli type sandwiches and salads, pastas, etc.
We had the QS plan last year and I don't think we had a hamburger, hot dog or chicken nuggets at all during our 8 day trip. Wolfgang Puck at DTD has excellent food. In Epcot almost every country has a great counter service and Sunshine Seasons in the Land pavilion is set up like a food court with a few different options. Flame tree BBQ in AK has great food. We even had a steak dinner at the American Pavilion in Epcot. I'm pretty sure that all of the resorts also have counter service meals. Check out the menus on the links that PP has posted.
As others have said, there are a lot of places with a variety of options other than burgers and hot dogs. I agree that Wolfgang Puck Express in DTD is a great choice for CS. It's one of our favorites and is a must do for us at least once every trip.