[VadeRetro]

It's precision, not accuracy, and the graph is meaningless without mentioning the confidence interval. There is an indeterminant error.

From the article:

The two most accurate measurements have experimental errors of 1 part in 10,000, yet their values differ by 10 times that amount. So physicists are left with no idea of its absolute value.

The error bars are far smaller than the difference between the most accurate existing measurements. For sure, more data is needed. Two points are not enough.

[RightWhale]

Technically speaking, it is precision, not accuracy. There is an indeterminate error somewhere. The error could be in an unsuspected factor in the theory, but it doesn't have to be. The error could be in one or the other lab setup, in the gear, in the treatment of data reduction, or in lax application of rules of statistical error.