As for the technobabble, a better phrasing is “Time runs more slowly for an object when it is in in a deeper gravitational potential than the observer.” Because when you are deep in a gravitational potential, everything runs more quickly than if you weren’t as deep.

If Chu watches a soccer game every week, should citizens complain?

If Chu spends every Saturday afternoon doing physics research, should citizens complain?

Science can be done as a hobby.

Also, Julian Schwinger had an idea about the Mossbauer effect that went against his contemporaries, whereby there is no initial impulse on one atom from the decay that is transferred to other atoms of the lattice but rather the impulse is on the whole ionic lattice through their quantum superposition. That idea now sounds sounder, at least to me, since I heard that the protein folding problem was recently ‘solved’ by two Chinese physicists. If large protein molecules can select a shape via a large superposition, such effects should also be present in metal lattices. So maybe the Mossbauer effect has a similar explanation, and that might affect the definition of a Mossbauer clock.

Anyway, in GP coordinates (which of course give the same physical results as any other GR coordinate choice), the gravitational potential does not change the time rate of clocks. Instead, objects closer to the gravitating body are modeled as moving. So the effect on clocks becomes a pure Doppler effect (the test body closer to the gravitating body is the traveling twin). This is basically a question of the universality of free fall.

I think that the real point of the Wolf et al paper is not that the experiment doesn’t measure anything, but instead that we’re lacking a theory that would predict a difference. If there’s any problem, it’s with the imagination of the gravitation theorists.