The 28% claim is wrong. It seems to be based on a common misunderstanding of how overhead rates are calculated.

In the supplementary table cited as the source, 72.1% of the total costs were awarded as direct costs and 27.9% as indirect costs (NIH, around 2020). That means an average overhead rate of 38.7% over all grants. Because some grants (such as equipment grants) have lower overhead rates, the average over grants with a normal overhead rate is higher.

At my (unexceptional public R1) university, the latest negotiated rates are 56.5% for on-campus research and 26% for off-campus research. The latter is lower, because many expenses that are normally covered by indirect costs become direct costs in off-campus research.

Unsurprisingly it appears the universities with the most advanced facilities/equipment and are therefore able to conduct the most advanced research have the highest overhead rates.