Just because you don't understand it doesn't mean that it is nonsense or wrong. If there is any lesson of the past century it is that everyday physical intuition is not useful in physics.it just doesn't sound right, based on nothing more than intuitive discrimination.
To me, the idea of bending/folding/warping 'space-time geometry' is a non-sensical statement.
This is not even self-consistent. "Shortest way" and "straight line" are both geometrical statements, so space must have geometry. I don't think you can say anything physically useful about space without making geometrical statements.Why does space have to have a geometry at all? Surely between the Earth and say, Neptune, there is just empty space in the main and that the shortest way to get there would be in a straight line (orbital mechanics not-withstanding).