That there's stuff that has a mass but doesn't interact well with light, or that space is able to curve itself without mass, thus also rendering Einstein false.
This immediately raises further questions: How long does space remember? How's the exact mechanism? Where and how does empty space store that information? What happens to E=mc2?
Clearly, Occam's Razor can only be applied correctly if you can distinguish what you really know from what are actually your assumptions. Not only do people hear what they want - but those who don't know don't know they don't know.
However, I get suspicious when someone argues by analogy. Your "my car remembers a crash, furthermore humans do remember, therefore space could also remember gravity" does not seem reasonable to me.
I am also not sure why my post got downvoted.
Edit: As I think about it, "but Einstein showed that you can bend space without mass" again is an argument by analogy. It doesn't matter what analogies exist. The theory should be tested according to empiric evidence. Pulling your analogies together judt for the sake of abandoning a different theory - where's the point in that?
Did you mean the metric tensor g_{\mu\nu} or the Ricci curvature tensor R_{\mu\nu}?
"Gravitational field" is one of those shifty things in GR that makes one sympathetic to MTW's refusal to identify the term with any particular mathematical object.
You're right though; there are plenty of exact solutions to the Einstein Field Equation which are vacuum solutions -- no matter, just gravity.