What is a bit more controversial is that model-dependent realism does imply that it's somewhat meaningless to discuss the "reality" of the situation. Instead, the only meaningful thing you can talk about is the usefulness of the model.
Many scientists that I've met do assume that he physical models which they work with represent the actual underlying physical reality of how nature operates. The problem, of course, is that scientists of the past have also believed this about their own theories and in almost every case their models have been shown by later research to have been incomplete.
Hawking & Mlodinow on Model-Dependent Realism
The phrase "model-dependent realism" appears to have been coined by Stephen Hawking and Leonard Mlodinow in their 2010 book The Grand Design. Here are some quotes related to the concept from that book:
"[Model-dependent realism] is based on the idea that our brains interpret the input from our sensory organs by making a model of the world. When such a model is successful at explaining events, we tend to attribute to it, and to the elements and concepts that constitute it, the quality of reality or absolute truth."
"There is no picture- or theory-independent concept of reality. Instead we will adopt a view that we will call model-dependent realism: the idea that a physical theory or world picture is a model (generally of a mathematical nature) and a set of rules that connect the elements of the model to observations. This provides a framework with which to interpret modern science."
"According to model-dependent realism, it is pointless to ask whether a model is real, only whether it agrees with observation. If there are two models that both agree with observation ... then one cannot say that one is more real than another. One can use whichever model is more convenient in the situation under consideration."
"It might be that to describe the universe, we have to employ different theories in different situations. Each theory may have its own version of reality, but according to model-dependent realism, that is acceptable so long as the theories agree in their predictions whenever they overlap, that is, whenever they can both be applied."
"According to the idea of model-dependent realism ..., our brains interpret the input from our sensory organs by making a model of the outside world. We form mental concepts of our home, trees, other people, the electricity that flows from wall sockets, atoms, molecules, and other universes. These mental concepts are the only reality we can know. There is no model-independent test of reality. It follows that a well-constructed model creates a reality of its own."
Previous Model-Dependent Realism Ideas
Though Hawking & Mlodinow were the first to give it the name model-dependent realism, the idea is far older and has been expressed by previous physicists. One of my favorite examples is a Niels Bohr quote:
It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature.