Higher rated capacitors = closer tolerances?

not true

The material the capacitor is made of has the biggest influence on the tolerance. How it's made is the next biggest influence.

It's pretty hard to make a really big, really accurate capacitor, so you don't find a 1.0000000 farad capacitor.

Most high accuracy capacitors are made for low voltage circuits, but at least in theory, you could make a high voltage high accuracy capacitor.

But a .01ufd at 50V isn't going to be inherently more accurate than a .01ufd 20V capacitor.