No, the "alternative hypothesis" as you state it doesn't fit the data, because it can be matched to any data whatsoever, it predicts nothing and anything. Dark matter models precisely fit the data and can be used to make accurate predictions about gravitational behaviour, so that's why they're considered useful. If dark matter actually exists as postulated, we would expect to observe precisely what has been observed up until the present with existing technology, so there's no reason to discount the model.
I have no problem with the idea of Relativity being incomplete and imperfect; we already know that to be the case, because it can't describe gravity and atomic phenomena together in arbitrary settings. But there are good reasons to consider or demand alternate theories, and there are bad ones; not having a complete picture of how something works is a bad reason to throw away a theory that works perfectly in countless other situations and can be readily tweaked to account for the unexplained phenomena in question.