This paper considers stabilization of fully actuated rigid-body attitude dynamics in the absence of angular velocity measurements and presents new robustness results to bounded unknown external disturbance torques. In particular, it is assumed that only body orientation is measured in the form of a unit-quaternion signal. It is well known that the passivity properties of the dynamics allows design of velocity-free controllers using a first-order stable filter driven by measured states. When external disturbance torques are taken into account, however, the robustness properties of these passivity-based output feedback controllers cannot be readily analyzed because the Lyapunov-like function from which the controller is derived has a time-derivative that is only negative semidefinite, and therefore non-strict. This obstacle is circumvented through a new partial-strictification approach which ultimately allows the characterization of robustness properties for this closed-loop system.