We resolve the long-standing open question of how the transport model AMPT manages to generate sufficiently high elliptic flow (v2) in A+A reactions with only few-millibarn 2->2 partonic cross sections - in apparent contradiction with an early study by Molnar and Gyulassy. Through detailed comparisons with the covariant Molnars Parton Cascade (MPC), we pinpoint which features of initial conditions, interactions, and dynamics encoded in the partonic stage of AMPT allow it to circumvent the opacity puzzle at RHIC.