No. I was referring to the "standard concentration bound" in that paper, which applies when you have separate validation and test sets. I think the argument can usually be improved by applying small-variance inequalities such as Bernstein's, to excess risk-like quantities such as l(f_hat(x), y) - l(f_ref(x), y), to show that accuracy difference / relative rank enjoys better guarantees. For ImageNet we can use the 01 loss and set f_{ref} to a SoTA classifier which, while having its loss bounded away from 0, is "mostly similar" to most f_hat's, and thus leads to a small excess risk.

The CIFAR experiments I mentioned were https://arxiv.org/pdf/1806.00451.pdf. It doesn't contain this argument (unfortunate wording) but appears to support it well.