In models of supersymmetry (SUSY) breaking and mediation, strongly coupled SUSY-breaking sectors can play a significant role in determining the low-energy spectrum of the model. For example, strong dynamics may provide a natural solution to both the SUSY flavor problem and the mu / B mu problem. Recently, it has been suggested that a large class of these models lead to identical boundary conditions at the SUSY breaking scale. These boundary conditions would severely constrain the models' viability. We demonstrate that the boundary conditions are instead sensitive to the details of the hidden sector, so that only specific hidden sectors may be ruled out by phenomenological considerations. We determine the high scale boundary conditions using the operator product expansion of the hidden sector. The techniques used to determine the beta functions are generally applicable to the RG flow of any approximately conformal hidden sector. The discrepancy with previously proposed boundary conditions can be traced to the fact that the renormalization group (RG) flow involves multiple fixed points. Show Partial Abstract