I don't think ROOT is very common in the atomic community. For experimental control, LabView is quite common, and it seems to have pitfalls too. But from what I know, the experiment itself is very straight forward, there are not so many places error can hide. Especially since they can calibrate/cross check everything with known H20 lines.

On the electron scattering side, ROOT is more common, but the experiments which are most relevant for the radius either predate ROOT or are known to not work with ROOT. Doesn't mean the software used has no errors, quite the contrary, however since all the results from different measurements with different software agree, I think a programming error is not the culprit.

Sadly, ROOT is generally-speaking the best part of physics code...if it were me, I would ask that all software used to derive a result be made available. It's far too easy for scientists to make stupid errors in their coding and it cannot hurt to be open.