Mathematical models can explain it all?

Over at the Statistical Modeling, Causal Inference, and Social Science blog, there is a discussion about the over-reliance on mathematical models to explain natural phenomena.
I like this passage by Stan Salthe, the author of "Why Mathematical Models Just Don't Add Up"

"In spite of the fact that qualitative models produce better results, our society as a whole remains overconfident about quantitative modeling. [...] We suggest applying the embarrassment test. If it would be embarrassing to state out loud a simplified version of a model's parameters or processes, then the model cannot accurately portray the process. [...] A scientist who stated those assumptions in a public lecture would be hooted off the podium. But buried deep within a model, such absurdities are considered valid."