This looks like a paradox, but it has a simple solution in GR: if your whole universe is filled with matter, it contracts. There is no orbit with a single particle, but two test particles would still move together faster than without the dark matter - or get different orbits.Here's a thought experiment. An otherwise empty space is filled uniformly with dark matter. We introduce a test particle.
Choose an arbitrary spherical region of space. According to your argument, mass of all dark matter inside that region will attract the test particle, and therefore test particle will orbit that region (or fly on hyperbolic trajectory). I.e. test particle won't fly in a straight line.
Which is obviously ridiculous.
You don't need inhomogeneous distributions. A finite ball with constant density (like a galactic halo) gives the same effect - two test masses feel tidal gravity which looks like an attraction between them.