TTo answer my own question 😺 ... I think it comes down to the different direction of the curl of the magnetic fields caused by the conduction current density (μJ) and the displacement current from (-$\frac{\partial E}{\partial t}$).
The curl of the magnetic field caused by the conduction current density is in the direction of the current (z direction) but the direction of the curl of the magnetic field from the displacement current is in the radial direction (ρ) of the E field. (The magnetic field lines in both cases are coaxial with the center conductor of course)
(there is a magnetic field with curl in/on the cable but a magnetic field without curl in the dielectric from the conduction current.)
When deriving the integral form of Ampere/Maxwell we use Stokes' theorem and integrate the curl component normal to the surface, over the surface, to get the line integral of the magnetic around the boundary. If this surface is bounded by the Amperian loop coaxial with the center conductor, then the curl of the magnetic field caused by the displacement current (which is radial) has zero contribution normal to the surface and thus plays no part in the calculation. Therefore, although the magnetic field in the dielectric has curl in the radial (ρ) direction, it plays no part the calculation of current in/on the center conductor.
This make intuitive sense when also considering the L/C lumped circuit representation.