If a scheme had something like that property and satisfied some simpler conditions, I would wager that it necessarily is a good compression scheme. However, this is very much not required of a good compression scheme:
Imagine that a compression scheme used the first bit to indicate if the encoded image is an image of a cat or not. Changing that bit would then have very obvious and significant implications on the encoded image.
If that example seems too unrealistic, imagine a modification of a compression scheme that, before decoding, xors every non-first bit with the first bit. Then flipping the first bit in the modified scheme is equivalent to flipping a lot of bits in the unmodified scheme, but they are equivalently good at encoding images.
Edit: To put it short, the important property is that equally-long encoded images are "equally plausible": it's not important how many bits differ between them, and it doesn't matter if they are similar to each other.
Ah, thank you. I misread the GP. It seems that he is saying nearly[^] exactly what I wanted to say in the edit.
[^] the property should hold not only for single-bit changes, but all length-preserving changes -- it's perfectly fine for all single bitflips to e.g. result in invalid codestreams.
Imagine that a compression scheme used the first bit to indicate if the encoded image is an image of a cat or not. Changing that bit would then have very obvious and significant implications on the encoded image.
If that example seems too unrealistic, imagine a modification of a compression scheme that, before decoding, xors every non-first bit with the first bit. Then flipping the first bit in the modified scheme is equivalent to flipping a lot of bits in the unmodified scheme, but they are equivalently good at encoding images.
Edit: To put it short, the important property is that equally-long encoded images are "equally plausible": it's not important how many bits differ between them, and it doesn't matter if they are similar to each other.