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TrickyDicky said:You hinted at it when you said: "Why couldn't there be dark matter whose ONLY interaction with ordinary matter is gravitational? Then we would never detect it by any other means than its gravitational influence."
In that case the explanation would point to a modification of our understanding of gravitational influences in galactic and supragalactic scales; and I don't mean MOND but I'd guess something more intrinsically related to spacetime curvature.
This doesn't follow. Otherwise identical galaxies have different dark matter fractions. That's very hard to fit with only changes to gravity.