This was the way I've always explained the battery thing. For a more lore-friendly reason, one could say the humans just don't really understand why the machines are keeping us alive, and so make the best guess they're using us literally as batteries.

"I suppose it could just be a myth, but I always thought that was the original premise and it was hollywood execs who insisted on making the matrix about batteries on the assumption that audiences wouldn't understand the concept of neural networks"

It's a myth. It was always batteries in the script, but when Neil Gaiman was hired to do a Matrix short story he added lines about using the humans as a neural network because he thought the battery thing was stupid. I've seen this well documented online so you should be able to find it if you try.