That's sounds exactly like what someone trapped inside a singularity would say.

Hmm, but what if the Earth has not been destroyed by a singularity yet?

We are at the center of what we can observe, obviously, but assuming that everything (including what we can not observe) is within the event horizon of a singularity then what we can observe may all be experiencing the same (relative) spacetime curvature and is apparently "expanding" because it is accelerating as it falls deeper into the singularity.

I'm kind of thinking of the classic spacetime expansion demo of dots on the surface of a balloon, extended into 3(+?) dimensions... the singularity (the balloon) is expanding as we (and everything else) are drawn further into it, resulting in the objects we can see (the observable universe) appearing to accelerate away from us. The actual center of the singularity is so far away that we can't observe it, and the acceleration appears (locally) uniform to us in the same way that the surface of an infinite-radius sphere would appear flat.

There's probably some obvious physics reason this doesn't work in reality, but I don't know what it is.