I think that might oversimplify things, in addition to being a model-laden description. There are empty-space solutions to GR (and indeed many a physicist has found the intuition that there is nothing but empty space appealing, cf geometrodynamics) and in these situations spacetime itself interacts with itself, no particles at all.

In any case, I would say this is a somewhat bold description of what we know about gravity.

It's also worth pointing out gravitation waves are a thing (have been detected by LaWD or Laser Wave of Gravitation Detector). Does not mean it's not changing the spacetime shape, indeed, these are a type of ripple in spacetime as might occur if Sally Struthers did a jumping jack.