I saw a YouTube video where they said this was more-or-less the original backstory but then they changed it. I think it said that the People In Charge thought the 'living power source' would be easier for the audience to understand?
I don't have the link handy, and don't trust everything I read on the Internet, etc, etc.
But yeah - this makes so much more sense than breeding, raising, and feeding humans just to harvest their body heat.
I like to think the machines actually were using them for processing power, and the humans themselves just misunderstood (or oversimplified for Neo) what was actually going on.
According to Reddit…so, grain of salt…that is an urban legend, related to a Neil Gaiman short story that appeared on the Matrix promo website.
https://www.reddit.com/r/movies/comments/1amree7/theres_a_wi...