Sure, but it's precisely that difference which they claim to be measuring. Why does it matter that they don't also know some other value (the radius) to high ac

Sure, but it's precisely that difference which they claim to be measuring. Why does it matter that they don't also know some other value (the radius) to high accuracy? It's kind of like how a balance can measure the difference in force to high accuracy (and precision), but that doesn't mean we know anywhere near that much about the masses on the balance, and...it doesn't have to; you can just state that you know some delta accurately and not have to explain why that means some auxiliary measurement is probably precise.