To make it short (as this would deserve an entire post), let me first summarize the problem for the other potential readers.

The proton radius puzzle is that fact that measurements of the proton radius from many experiments using electrons all agree among them, but the numbers stemming from the sole experiment using muons disagree with all the others. This experiment is however way more precise than the electron-induced measurements (each data point as an error attached to it).
This remains one of the major puzzle of our field. One does not understand where the discrepancy comes from.

Maybe is this discrepancy due to new physics, maybe to some Standard Model contribution that has been missed (higher-order QCD corrections for instance) or maybe there is an experimental issue with the electron and/or muon measurements.

So far, all these explanations are equally good. Only the future will (hopefully) tell us.