Well, that's not actually true at all. There are very simple hypotheses motivating things like DARE or Scared Straight, for example. What happens is, you do an experiment, and those simple experiments don't work out the way you thought. And so you have to explain it, which requires a bit of work.
This isn't any different from other sciences, where you have one hypothesis, test it, and it doesn't go the way you thought, and then people are left scratching their heads for a bit, until someone guesses right and demonstrates it experimentally.
Those mathematical models in physics you mention we accept because of debates over which was correct, for example, followed by experiments (and observations!). You see gambles on explanations of unexplained results in molecular biology all the time that don't really involve the same level of mathematical precision.
I think you're overstating the extent to which scientific process occurs in all disciplines with very precise mathematical models with low stochastic error. As the complexity of your system increases, the residual noise in any given model, especially models with little established information, will be high.