The models of the universe with and without dark are fundamentally different, it is not inventing "invisible stuff to explain that the model is still right". The nature and composition of fundamental particles are an integral part of models of the universe. There is also a long track record of predicting the existence of particles and then later discovering these particles, for example the Higgs boson. Of course far more particles have been predicted and not (yet) discovered, such as theories of super-symmetry, but these predictions usually don't have the same type of consensus that the Higgs or dark matter has. While dark matter is invisible in the classical sense, it is observable by its gravitational effects. We have also observed what looks like clumps of dark matter, which modified theories of gravity have great difficulty explaining. With that said, until someone actually experimentally observes dark matter it is still a theory and could well be wrong. But this is true of all competing theories - there is no experimental evidence for theories other than dark matter.