It seems to me that the idea of dark matter grew from doppler measurements of the velocities of the outer stars of spiral galaxies. It was assumed that what was being measured was the orbital velocities around the galaxy's center.
The mass of a galaxy was assumed originally to be the sum of ordinary stuff (stars, debris, dust, black holes, etc.) and this mass's gravitational pull would not support the orbital velocities of the outer stars. Hence the idea of dark matter was proposed.
Is it possible that the outer stars are at or beyond escape velocity for an "ordinary" galactic mass and are simply moving outward rather than being in orbit? That they have been simply flung outward by some sort of pinwheel effect, perhaps off the ends of the inner galactic bar? In this case measurements of their velocities wouldn't be very useful in making assumptions about the galactic mass.