This is 99% urban legend. You can just barely create it in a lab with just the right plant (with thick hydrophobic trichromes) under just the right light with no wind... but that's not what happens in nature.
Exactly. When it rains in nature, 95% of the times a) there isn't enough sunlight for the droplets to focus and make a burn spot, and b) the droplets don't stay on the leaf but flow down instead.
The original advice is solid and not an urban legend, but it applies to cases like watering plants in your balcony when the sun is out, bright and hot. Source: I have caused burn spots in plants of my own.
I believe watering at night will generally lead to more fungal rot problems. Better to water early morning, when the water will have a chance to sink into the soil, but will be pulled up into the plant by evaporation of water from the leaves (the leaves’ own water, not water you applied)
