Attractive colloidal-scale forces between macromolecules in biological fluids are suspected to play a role in important system dynamics, including association times, spatially heterogeneous viscosity, and anomalous diffusion. Passive and active microrheology provide a natural connection between observable particle motion and viscosity in such systems via generalized Stokes-Einstein and Stokes' drag law relations. While such models are robust for purely repulsive colloidal-scale interactions, no such theory exists to model the effects of attractive forces. Here we present such a model for the linear-response regime, where a Brownian probe particle is driven gently through a complex fluid by an external force that weakly augments thermal fluctuations. As the probe moves through the bath, hard-sphere repulsion results in an accumulation of particles on its upstream face and a trailing depletion zone, producing particle drag that slows the probe. Linear-response viscosity can be inferred constitutively from this speed reduction. One expects attractive forces to make the suspension more viscous, but surprisingly, weak attractions exerted by upstream particles actively pull the probe forward, giving it a "hypoviscous" environment through which it slides more easily. As attractions grow stronger, particles join to the probe in a long-lasting doublet, extracting particles from the upstream region and depositing them behind the probe. At a critical value of the second virial coefficient common to all potentials we studied, the distorted structure reverses direction, and continued growth of attraction strength causes the probe to drag a cluster of density along, dramatically increasing viscosity. But at this transition, the structure is neutral under the balance of attraction and repulsion, allowing the probe to "cloak" itself and move through the bath undetected and unhindered relative to hard-sphere dispersions. This poses an intriguing mechanism by which proteins or other macromolecules may change their surface chemistry in order to alter the viscosity of the surrounding medium to speed their own motion, or simply to pass undetected through a cell.