Here's a simple diagram:

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The oil pump reduces pressure at point I and increases pressure at point O. This is a pressure differential maintained by the power delivered to the pump. Suppose ambient pressure is Pa. The pressure we measure with a gauge at point O is Po, and at point I is Pi. Because we measure it with a gauge, that is relative to ambient pressure Pa. So the absolute pressure at point O is Po + Pa, and at point I is Pi + Pa.

For example suppose Po is 30 PSI and Pi is -10 PSI. The pump delivers 30 PSI of oil to the engine, creates 10 PSI of vacuum to draw fresh oil from the intake, and maintains a pressure differential of 40 PSI.

The question is, how does Pa affect this? The pressure difference across the pump is Po - Pi. It is independent of Pa. Any change in Pa changes Po and Pi equally. Put differently: if Pa drops, the pump has more resistance on the intake side and less on the output side. And vice versa. All forces in balance, no net change in the pressure differential across the pump, or the power needed to drive it.