I really don't like to get involved in these "weight police" discussions, but one should understand that GVWR on these trucks is somewhat of a manipulated marketing and legal number. In this instance, 10,001 to 14,000 lbs GVWR is a Class 3 vehicle, while 14,001 lbs GVWR to 16,000 lbs moves up to Class 4. This has registration, licensing and other implications that may not be reflective of the true capacity of the truck. Payload capacity is a derivative of GVWR as it equals GVWR minus manufacturer's curb weight plus an allowance for a 150 lb driver.
So, yes, one can claim that a truck is "overloaded" if it is over its manufacturer's GVWR or payload ratings, but it should also be understood that those aren't hard "mechanical capability" ratings like the front and rear axle GAWRs. It is commonplace for Class 8 rigs to have a GVWR that is the arithmetic sum of the GAWRs.
Rusty