This is not my field, but I think it is as simple as a combination of the things you said - accurately estimating the amount of "normal matter" within the solar radius, accurately measuring the rotation curve (different tracers can give slightly different results), but mainly that dark matter does not dominate the dynamics at small radii.
For instance we know what the mass density is in the local disk by looking at the velocity dispersion of stars perpendicular to the plane (e.g. Kuijken & Gilmore 1989; Creze et al. 1998). These results show that dark matter is hardly present in the disk at the radius of the Sun - the local mass density is entirely accounted for by stars, gas and stellar remnants.
There is no real reason why the (dissipationless) dark matter should be as centrally concentrated as the luminous matter, and that appears to be the case.
Models for the Milky Way dark halo suggest it is distributed with far less "concentration" than the mass in the disk. The scale length parameter of the Navarro-Frenk-White profile is typically found to be $\sim 20$ kpc (e.g. Klypin et al. 2001), whereas the exponential scale length of the disk is more like 3-4 kpc. The plot below shows how various components contribute to the rotation curve. See how dark matter is only dynamically important at large radii, beyond the solar orbit. So I think that even if you have very good measurements it is still difficult to get a handle on the dark matter profile from the rotation curves because it doesn't change the overall rotation curve prediction that much at small radii.