QED is not endangered by the proton's size

Pohl et al. have reported a very precise measurement of the Lamb-shift in muonic Hydrogen, from which they infer the radius characterizing the proton's charge distribution. The result is 5 standard deviations away from the one of the CODATA compilation of physical constants. This has been interpreted as possibly requiring a 5.9 standard-deviation modification of the Rydberg constant, to a new value that would be precise to 3.3 parts in $10^{13}$, as well as putative evidence for physics beyond the standard model. I demonstrate that these options are unsubstantiated.