Still wrong. While it is still restrained by the rotating system, the force - or lack of force - on the valve is outward. If your valve were to go flying off your wheel, it would no longer be part of the rotating reference frame and would fly off at a tangent, but if that happens you have bigger things to worry about.

Construct the setup in a rotating reference frame, where centrifugal force is quite useful, and it shows up clearly. Centrifugal force doesn't exist in an inertial frame, but it does in a rotating frame - where does it come from?

What you are forgetting this time is that the wheel itself is moving. An in inertial reference frame, all parts of a rotating wheel are constantly being accelerated towards the center. The valve's inertia resists this inward acceleration. It still wants to fly off at a tangent. It is the lack of a force pulling the valve inward at the same rate as the rest of the rim that causes "centrifugal force", and it "pushes" the valve open, opposite the centripetal force on the rim.

This is why rotating reference frames are still useful - humans have a harder time visualizing the forces in an inertial one with rotating systems.