Yes, I agree that there is no requirement, merely responsibility. Reponsibility is far far different from rights.
Rights are legal entitlements such as life, liberty, and the pursuit of happiness .
So to say that an animal has rights when you are simply invoking reponsibility is incorrect. We all live in an ecosystem of mutual dependence. The way that one chooses to respond to pain in any organism must be balanced against the goals of the ecosystem. Even if I completely ignore the ecosystem I am still part of it. So if I am a hunter I am still part of the ecosystem.