algorithms – Question in coreset construction fro K-median clustering

I was reading Ke chen’s paper about coreset construction for K-median clustering. In this paper, he assumed that $A$ is an $(α, β)$-bicriteria approximation for K-median clustering for some $α, β=O(1)$. I am wondering if the construction still work if $A$ is an arbitrary set of $αk$ centers?
Can anyone help prove the correctness of my suggestion?