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I haven't heard anyone point out that it is not the mass of the ball rolling down the hill (or the comet striking Jupiter, or the neutron being captured by a proton) that changes it's "invariant" mass, but the *system* of the ball plus the earth, which due to the fact that they are now more tightly bound together than they were before have, collectively, less mass than they did before. We cannot assign that mass change to either object, although I guess it would be possible to assign it in proportion to the initial mass of each. I'm not sure how this would work out, but what is relevant in the potential energy case is the total mass of the system, and not the individual masses of either object.
It may also depend whether you consider all forms of potential energy contribute to mass. Some may allow only certain forms of potential energy. Some may regard a ball moving down the slope, losing its potential energy, and hence losing invariant mass.