Flow increases as pressure decreases.
This isn't right, or at least not the entire picture.
This says that if pressure goes to zero, flow is infinite.
Pressure build up in a fluid is a result of the forces applied to the fluid. Some of that force is from the pump and some from the constraints of the container.
If the force goes to 0, then there is no pressure and no flow.
I'm not an engineer, but it seems that maybe what we are really after is a sufficient flow of oil at the bearing surfaces and other lubricated areas and not necessarily pressure. Pressure is probably just easier to measure, and given that everything else is relatively constant (oil passage cross sections, oil viscosity) serves are a proxy for flow.
I suspect you could put really thick oil in your engine, have high oil pressure, and still damage the engine due to insufficient lubrication.