Doesn't Memento prove the opposite? The character was basically stuck in a loop, and was taken advantage of by someone who held the real agency. (Notwithstanding the "happy ending" conceit at the end that resolves the audience's uncomfortableness with this lack of agency by intimating he may still possess some minimal agency despite the big reveal.)
But in any event, drawing conclusions about the real world from a fictional story seems fraught.
Leonard was still an intelligent entity despite lacking the ability to learn.
In fact the amount of limited agency Leonard had is similar to the limits in agency we want for an agi that serves humanity.
Anyway my main point is Leonard has intelligence well past what we expect from an agi. So because people like Leonard are documented to actually exist one can say live learning is not really needed to have Leonard levels ( aka agi levels) of intelligence
But in any event, drawing conclusions about the real world from a fictional story seems fraught.