If bishops have the responsibility, we do know that in the era of retrenchment, the curia has or once had the authority. If the CDWDS hears a report, they communicate to the bishop, who investigates:
[181.] Whenever the Congregation for Divine Worship and the Discipline of the Sacraments receives at least a plausible notice of a delict or an abuse concerning the Most Holy Eucharist, it informs the Ordinary so that he may investigate the matter. When the matter turns out to be serious, the Ordinary should send to the same Dicastery as quickly as possible a copy of the acts of the inquiry that has been undertaken, and where necessary, the penalty imposed.
The bishop reports back to the CDWDS. So the chain of command is well-established. The complainers inform Rome, who directs the bishop to do the leg work and to submit a report.
There’s a bit more for super-serious cases:
[182.] In more difficult cases the Ordinary, for the sake of the good of the universal Church in the care for which he too has a part by virtue of his sacred Ordination, should not fail to handle the matter, having previously taken advice from the Congregation for Divine Worship and the Discipline of the Sacraments. For its part, this Congregation, on the strength of the faculties given to it by the Roman Pontiff, according to the nature of the case, will assist the Ordinary, granting him the necessary dispensations [Cf. Pastor Bonus 63] or giving him instructions or prescriptions, which he is to follow diligently.
And this basically seems to tell the local bishop that he is to follow orders when given them, because the CDWDS is the arm of the Pope. We will see if this survives the reform of the letter and spirit of Pastor Bonus, which, reportedly, is out the window when a new curial administration plan is put into place under Pope Francis.