There’s a lot here about the proton radius saga which isn’t captured in the article. The energy levels of hydrogen can be calculated from a closed-form analytic formula, which a function of the proton radius r_p. Thus by performing spectroscopy on different transition levels of hydrogen, one can (by inverting the formula) repeatedly measure r_p and compare the results. One can similarly do this for muonic hydrogen. This plot (from a review by Pohl et al.) captures the essence of the puzzle:
The blue dots are independent measurements of r_p (with 2 sigma error bars) taken since the 1990s by using different transition frequencies of hydrogen. The vertical blue line is the average of all these past measurements. The vertical red line is the very precise measurement from muonic hydrogen (which started the whole puzzle). As you can see, the muonic hydrogen value doesn’t deeply disagree with any of the blue values if you take them one by one, as the blue values have large uncertainties. It’s only when you take the blue values together and compare them to muonic hydrogen that you get the huge discrepancy. Is it statistically legitimate to average together the blue values together in that way? This was never clear to me (or several others that I talked to).
The proton radius puzzle continued with a different experiment of Pohl’s group (2016), this time using muonic deuterium. The measured of value of r_p was closer to the newer, smaller muonic hydrogen value. Even more surprising was a measurement (2017) by the Haensch-Udem group using the “traditional” methods of plain old hydrogen spectroscopy - the same method as the blue dots in the graph above. The result found was again consistent with the smaller value. The latest result in the article from York University is a measurement of r_p using yet a different method, and it is found to agree again with the newer, smaller value.
Despite the agreement on the smaller value for r_p using multiple methods published in the last 5 years, it’s unclear whether one can really say that the proton radius puzzle has been “resolved” other than sociologically. To this day no one knows what was wrong with the older hydrogen spectroscopy measurements which gave the larger values - perhaps some mysterious systematic error? Still, people seem more comfortable to trust recent results using state-of-the-art methods and modern standards of characterizing and reporting systematic errors. There is some sort of “recency bias” at work. This might be why the news article talks about the proton radius being “resolved” with the new Lamb shift result.
Still, there is one contemporary (2019) measurement of r_p which agrees with the older, larger value, performed by a different group in France. As far as I know, nobody has also been able to explain why this result, which disagrees with the two Pohl results, the Udem result, and the recent Hessels result, is wrong.
To me, the whole episode serves to show that even in the very meticulous field of precision measurement, there can be puzzling discrepancies in results, even if the measurements were all performed by highly reputable, experienced groups. There are limitations in our abilities to characterize and look for systematic errors. Thus, a single (or even a few) aberrant measurements are insufficient to convince the field that there is some new revolutionary physics going on. This is important to keep in mind especially in threads where people like @stcordova have questioned special relativity on the basis of a few aberrant experimental results.