The orbital period of a star in a galaxy depends, to first order, on the amount of mass that is closer to the centre of the galaxy than the star. (That's a consequence of gravity being an inverse-square force.)
The distribution of stellar orbital velocities in a galaxy indicates that there is additional mass, not at the centre, but distributed amongst the stars in a galaxy. An inventory of the visible mass shows there is nowhere near enough to account for the velocity distributions. Therefore, it is inferred that there is invisible, or dark matter, that accounts for the discrepancy. It has nothing to do with mismeasuring the mass at the centre of the galaxy, whether it's a black hole or not.
This also holds true for the affect of gravitational lensing produced by distant galaxies.