When the Universe is taken as a whole do the changes of gravitational energy in spacetime exactly cancel out the changes of matter energy (including dark matter) due to the expansion of spacetime? How do we know (is there some mathematical reason to believe this is the case)?

When the author says that spacetime absorbs matter energy or gives matter energy, what does that really mean? Does it mean it can be used as a convenient sink or well in regards to changes of potential energy? What are the rules governing that transfer or do we just make things balance and decide that spacetime did it?

I am trying to shake this uncomfortable feeling that it is too convenient. I'd love to know the ground those kinds of operations stand on.