You're seeing things correctly - but you're not looking at the big picture.
In our shop, we've got a fan that is rated for 0.036 psi of static pressure and 8000 cfm for dust control. It's 36" in diameter. The fan also has a damper a few feet after it for speed control.
When I close the damper completely, the duct in front of the damper will experience a pressure rise, almost to 0.034 psi. The duct behind the damper remains at 0 psig. Since this is the fan's top pressure it can push, and the pressurized air in the duct is pushing back on the fan, almost no air flows through the duct. Instead, the fan is mostly trying to keep the space between the fan and the damper pressurized. Think of this as potential energy (or voltage), and the damper is acting as a resistor removing that potential energy, with no current.
When I open the damper, the duct behind the damper still remains at 0 psi, but since I don't have a damper blocking the way, the air can come rushing out the fan at all 8000 cfm. The duct before the damper is nearly at 0 psi as well. So, the whole system is operating at a lower pressure, less than the 0.03 psi. There is no potential energy drop across the damper. But, instead of working like an electrical "battery", the fan operates on a fan curve and the pressure in the entire ducting system drops, rather than keeping the same "voltage" like you would be used to in an electrical system. But the energy is there - just converted from static (pressure) energy to dynamic energy.
The stators operate the same as the damper. Imagine if another fan grabbed that pressurized air between the fan and the damper and pushed that against another damper. Repeat as often as you want and you have high pressure air. The same concept, just two different applications.