I think the point is that the cooking process starts well before boiling temp. Potatoes take a lot longer to cook than corn so you would want to take advantage of that fact. Where corn cooks a lot quicker you would want to have a shorter cooking time to preserve the fresh flavor and texture so already boiling water helps that.
You can put potatoes in water that’s already boiling. It’s fine.
I think the point is that the cooking process starts well before boiling temp. Potatoes take a lot longer to cook than corn so you would want to take advantage of that fact. Where corn cooks a lot quicker you would want to have a shorter cooking time to preserve the fresh flavor and texture so already boiling water helps that.
Same for carrots
iirc there’s some (mainly textural) differences that make having potatoes stay somewhat below boiling for a bit better.