Precision results are usually blinded, so it's not as if scientists can just rejigger the calculation if it's giving an implausible result; once the result has

Precision results are usually blinded, so it's not as if scientists can just rejigger the calculation if it's giving an implausible result; once the result has been unblinded, the calculation is finished. The physicists working on these experiments are therefore extremely motivated to quantify all potentially non-negligible sources of systemic error beforehand. That said, the issue in this case is almost certainly systemic, not new physics. But I don't think you should consider the misfortune of the data-driven calculation typical; rather, it's notable specifically because of the discrepancies. Most calculations do not have such large disagreements. The lattice results, in contrast to those from the data-driven approach, all line up very nicely.