Test audiences will misunderstand the scientifically impossible explanation as much as they will misunderstand a plausible explanation, so why not use a plausible one?
"Humans are batteries when the sun goes out!" Is easy for people to understand.
"Human minds are computers but in order to use human minds as computers we need to make the matrix as a semi-corporeal realm, oh and this is why people like Trinity can do impossible things like jump really far because their minds are so powerful and actually used in the calculations of the matrix that they can impact it's outcome."
