This is the very reason why Wall Street firms hired physicists (and engineers). There was a report several years ago in Physics Today that stated that 95% of MBA's have no clue of the math being used in the derivative market. Yet engineers and physicists often deal with such 2nd order non-linear differential equations all the time, AND, have the need to have a "feel" for such particular models since these things typically represent some physical processes.
However, having said that, I still disagree that just because such a field are starting to adopt mathematical models and physics concepts, that it has attained a "rigorous" science status. It is one thing to come up with a mathematical model. It is another to actually reproducibly prove that the model is valid. This is where testing (what we in science would categorize and repeated experiment) of that model comes in. More importantly though is that in practically all cases, what the model represents is a phenomenological description, typically based on a previous set of data. As any scientist can tell you, an idea or theory or concept is never
rigorous if all it has is nothing more than phenomenology.