You are both right but it depends which generation of 737 you are referring to.
Quote from a certain book…
“With all pumps on, centre tank fuel is automatically used before main tank fuel. To achieve this, the NG centre tank pumps deliver at a higher pressure (23psi) than the main tank pumps (10psi). On the 1-500’s the centre tank pump check valves operate at a much lower pressure (1.3psi cf 12psi) allowing fuel to flow from this tank first.”
S&L