Yes, Dark Matter is a statement about the premise that something appears to be operating gravitationally while have no (or perhaps so little that we don't recognize it) interaction with other matter; however, it is not without reason.
The primary focus on matter as the candidate is that if you don't believe that some form of matter is responsible, you begin having to explain how a lot of our Laws are incorrect. Dark Matter is really a problem that we have a notion how our Laws should work at the cosmic scale, yet they don't. And yet, we don't see any obvious reason why they shouldn't give how thoroughly we've tests these Laws.
For instance, if you say that our equations for gravity is off, why is it completely consistent for everything in our solar system? Why is consistent down to the most precise test for gravitational frame pulling? It seems to be only different when you talk about very large masses creating gravity on objects tugged at very long distances. Why does it just cut over to different behavior?
If you say that gravity is emergent, then how do you explain the standard model's place for the graviton? Granted, it's not testable (gravity is so weak it's beyond direct testing), but it seems to be fit right in to a spin-2 tensor where we would expect a gravity-like particle to be. Why would you expect that to not be true?
That said, Dark Matter matter candidates are getting weeded out pretty quickly, these days. No new types of particles are being discovered, and Dark Matter observatories are largely coming up empty. But, that's science: got an idea? Test it and let the results speak.
As an aside, I think one thing to remember is: just because science doesn't know the answer to something, it often knows what can't be the right answer. Look into the theory's and their criticisms.