@ZachWeinersmith Not a cosmologist, but I’ll give this a crack.

Speed is a red herring here, you’re correct to note that scale is the only important factor.

Ever done calculus? At each point of a well-behaved continuous function, you can draw a tangent. That tangent will always be perfectly flat, no matter how curvy the function is, because that’s what “well-behaved continuous” means: zoom in closer and closer at any point, and it looks more and more flat.

Spacetime, according to GR, is also “well-behaved continuous.” Pick any point, and the more you inflate/scale the overall space, the more that point resembles its derivative. The local area “flattens out,” no matter how curved the original space was.