  We show that hyperrigidity for a C*-correspondence $(A,X)$ is equivalent to
non-degeneracy of the left action of the Katsura ideal $\mathcal{J}_X$ on $X$.
Due to the work of Katsoulis and Ramsey, our result shows that if $G$ is a
locally compact group acting on $(A,X)$ and the Katsura ideal $\mathcal{J}_X$
acts on $X$ non-degenerately then the Hao-Ng isomorphism problem for reduced
crossed products has a positive solution and the Hao-Ng isomorphism problem for
full crossed products has a partial solution.
