Well yes, this is the way we also understand it in the dojo I know:
It is ukes responsibility not to get hurt. This is what makes good ukemi so demanding.
For the most part, I basically agree with that... but since all grades practice together and there are no weight categories, I think it does sometimes need some common sense adjustment on the part of nage - you don't intentionally give someone way more than you have reason to believe they can likely handle, particularly someone less experienced than you.
E.g., I think your statement applies differently if nage is a shodan and uke is a fifth kyu, versus two dan ranked students together.