The Matrix
ISTR reading that that’s the original explanation, and it is what the depiction of the programs-as-people (and agents specifically actively replacing people) is grounded in. The exposition—but just the exposition—was changed at studio direction based on test audience feedback.
(Personally, I think the change to in-character exposition is an improvement, not because it is plausible, but because it foreshadows and underlines that the “free” humans understanding of the Matrix is ultimately grounded in deception intended, as later made explicit, a system of control.)