That's intuitive but doesn't support the result of the lucky subnetwork (once found and re-initialized) training faster and outperforming the original.
This does not seem to be a contradiction. Once you are in the right region of solution space training is expected to be faster and easier. Re-initialization could have a regularizing effect, explaining the better performance.
They re-use the same initialization, so it appears that the initial weights are inherently coupled with the nonzero structure.