We study a fully parabolic predator-prey system with indirect pursuit-evasion behavior under Neumann boundary conditions. Strong coupling between the predator and prey densities, induced by a Holling type I functional response, is a key feature of the model. In contrast to most of the existing literature, which concentrates on the case of strong logistic growth, we develop a complete solution theory for the weakly damped logistic situation. It is shown that appropriate sub-logistic damping can prevent blow-up in two space dimensions, while for any quadratic logistic degradation the system always admits global weak solutions in higher dimensions (N≥ 3).