I wouldn't classify rats<->humans as an analogy in this context. Generalizing (too broadly, probably) premodern medical "science" was explicitly analogical in many ways, e.g. "we will use this herb that looks like an eye to cure your eye trouble" but that is obviously completely different than the experimental/genetic basis on which we use rats as a medical model for humans.
OTOH, since arguing over semantics is mostly a waste of time, if you want to call it an analogy, then fine, but I would say you need to drop your "mere" from the original article, which is doing a lot of the work in that argument, since clearly analogies in your view are quite powerful, have predictive power, etc. I hope this doesn't come across as overly pedantic, I just find thinking about these things very interesting.
Not sure I understand your point about such models needing to be robust in the face of different parameters. I was working on a model the other day which I discovered had very different behaviour based on the initial parameters in a way that will have direct impact on the software I'm writing/business process I'm developing, making it safer and more predictable. Maybe that outcome should have been obvious, but it wasn't to me (or at least, I suspected something like it, but wasn't able to reason through to the conclusion without the aid of a model). In this case, I consider the fact that different predictions were made based on altered initial parameters to be a strength, not a weakness. But going back to your point "you should only give it force if the stories it tells are plausible in light of your experience and knowledge," I agree and if the model were outputting very surprising and counter-intuitive predictions, I would start by assuming the model was wrong, not my intuitions.