Adding to what Dick said -

If you write out the equations for flutter, and I won't, there are mass terms, and moment arms of those masses that determine when the moment of inertias and when flutter will occur. Of course the speed is a factor as well as the flexibility of the surface and slop in the linkages.

Getting the center of mass over the hinge line removes the weight plus moment arm. The moment of inertia is still there but much reduced in magnitude.