I'm guessing that Sagawa got it from Sokaku Takeda, and that the concept and method itself initially came from China.One thing that breath is very useful for, in beginners, is as a vehicle for learning how to "drop" one's "innards" downward, a precursor for one kind of power production. After a while, once you gain awareness of what's moving inside, and how, you no longer need to use the breath as vehicle or guide; intent is sufficient to fire the internal movements to manipulate your "innards." That might have been one thing that Sagawa had in mind when he made his comment on breath work.
Actually, it seems from the article here, that Sagawa spent extensive time exploring breath power, and at length determined, for himself, that it is optional. While I have no doubt that this originated as some Taoist practice in China, I wonder if this was actually an enunciated part of Takeda's system.