you can most definitely change the levels of components in a fried food.

the oil gets 'dirty' from extended use in frying. Why is it dirty? It's not dirt, and it's not oil breakdown (in most cases).

The oil is drawing components from the food into itself.

Forget the frying for a second; most fries are parboiled or blanched -- this also leeches material away from the vegetable, this time it leaves with the water used for blanching.

A french fry is delicious, but it's different than a potato -- even if it's made from one.

I don't know about the case of potassium specifically, but in general I thought that the bioavailability of elements can vary with different types of cooking?

Why would something being an element mean that heating it as part of a food wouldn’t act as a catalyst for some chemical interaction?

I guess that depends how hot you fry it.