2007 Volkswagen Passat Engine Failure

I own a 2007 VW Passat Wagon 2.0T. It has 42K miles and we have kept up with all services and recommend 10K oil changes. While driving the car just died with no indicator lights at all. Now the dealership has the car and says it holds 5.2 qts and only has 1.7 qts in it. It has been 6 months and right at 10K miles since the last oil change. They are claiming b/c the oil was low and we did not check it that it caused damage to the engine - something about the cam and some head on the engine and will be a minimum of $4200 to repair. They will not honor the warranty (we purchased an extended warranty) b/c the oil was low. My question is should the car burn this much oil and could an engine problem be the cause of the oil being so low in the first place. I feel like we are gettin the run around and be taken advantage of b/c we do not know that much about cars.