A hypothesis that explains the perceptions can be a just-so story. For any set of perceptions ζ, there may be a vast number of hypotheses that explain those perceptions. How do you choose among them?
In other words, if f() and g() both explain ζ equally well, but are incompatible in all sorts of other ways for which you do not have perceptions to distinguish them, ζ may be “evidence for the hypothesis” f and ζ may be “evidence for the hypothesis” g, but ζ offers no help in determining whether f or g is truer. Consider e.g. f is idealism, g is realism, or some other incompatible metaphysical positions that start with our perceptions and speculate from there.
An author I read recently compared this obstinate coherence of our perceptions to a GUI. When I move my mouse pointer to a file, click, and drag that file into another folder, I’m doing something that has predictable results, and that is similar to other actions I’ve performed in the past, and that plays nicely with my intuitions about objects and motion and so forth. But it would be a mistake for me to then extrapolate from this and assume that somewhere on my hard drive or in my computer memory is a “file” which I have “dragged” “into” a “folder”. My perceptions via the interface may have consistency and practical utility, but they are not themselves a reliable guide to the actual state of the world.
Obstinate coherence and persistent similarity of structure are intriguing but they are limited in how much they can explain by themselves.
It sounds like you want to say things like “coherence and persistent similarity of structure in perceptions demonstrates that perceptions are representations of things external to the perceptions themselves” or “the idea that there is stuff out there seems the obvious explanation” or “explanations that work better than others are the best alternatives in the search for truth” and yet you also want to say “pish, philosophy is rubbish; I don’t need to defend an opinion about realism or idealism or any of that nonsense”. In fact what you’re doing isn’t some alternative to philosophy, but a variety of it.