There are many forms of noodle soups. One style is to cook the udon or soba noodles, pour off the boiling water, and then, depending on the particular variant:
1) chill in cold water. then pile on the soy souce, spices and veggies, whatever else is going in. no stock.
2) pour on top the of the cooked noodles the stock, veggies, and the other ingredients.
The result is a chewier noodle, and it is more ingredient-centered than soup-centered.
The soup is japanese. The word to describe the method of preparation- *splashing* the ingredients & stock on top of the cooked noodles- is a common one. Yes, it's unfortunate that a certain industry has latched on to the word for something completely unrelated. I'm sure this is why one rarely sees this style of soup listed on a menu. As I mentioned, I have only seen it on the menu locally at Mikaku Sushi Taro.
The world is full of words that someone has appropriated to mean something offensive to *someone*. That shouldn't mean oblivion for the original legitimate usage of such words.