> I don’t know how to trust the author if stuff like this is wrong.

She's not wrong.

A good way to do this calculation is with the log-ratio, a centered measure of proportional difference. It's symmetric, and widely used in economics and statistics for exactly this reason. I.e:

ln⁡(1.2/0.81) = ln⁡(1.2)-ln⁡(0.81) ≈ 0.393

That's nearly 40%, as the post says.