I apologize for mixing the the term center of pressure here. My point is to ilustrate that there is a difference of pitching moments according to the airfoil selected. If the same CG is maintained while changing the shape of the airfoil the pitch will be affected. Take this two airfoils used in the design of an aircraft named "One Design" featured in Sport Aviation february 1994 edition.
The NACA airfoil has the max thickness at 30% while the "one design" has it at 20%. As you can see the moment coefficient is positive and keeps increasing as the AOA increases while the "one design" coefficient goes negative until it reaches 14 degrees. Adding this pitching moment to a 3D model which tends towards neutral stability can bring it towards the negative stability region.