There historical precedent for assuming your theories/models are just fine, but some invisible stuff is causing your observations to not match the math. For example, in the late 1700s when astronomers noticed Uranus's orbit wasn't following Newton's equations, some of them suggested another planet was out there disturbing things with its gravity - so basically Neptune was dark matter for several decades until they directly observed it. Another would be when Pauli noticed that beta decay didn't seem to follow the conservation of momentum; he predicted what we now call the neutrino was carrying the momentum away.
Of course, sometimes you do need a better theory; see how relativity was needed to explain Mercury's odd orbit, not another planet. That said, various forms of indirect evidence seem to strongly point to the dark matter hypothesis versus any of the modified gravity theories. For example, a small number of dwarf galaxies have been discovered that don't have the galactic rotational curve problem that other very visually similar galaxies do, which can be explained with the dark matter theory readily enough (those galaxies just have little dark matter for some reason), but are a bitch to shoehorn any modified gravity theory into.
