I think a more nuanced way of defining iii is that the intelligence an agent is capable of is limited by the extent to which it is capable of perceiving and interacting with an environment.

At one level this has to be true, if it weren't I could plop a black box on the table and say I've invented AGI it just can't interact with anyone, and you would have no recourse but accept my statement. We must necessarily define intelligence as the interaction that the agent can perform with some environment otherwise we'd have no way to know of its intelligence.