At first glance, this brief section seems to suggest lay people will join clergy in policing who receives and who doesn’t:
42. The safeguarding and promotion of ecclesial communion is a task of each member of the faithful, who finds in the Eucharist, as the sacrament of the Church’s unity, an area of special concern. More specifically, this task is the particular responsibility of the Church’s Pastors, each according to his rank and ecclesiastical office. For this reason the Church has drawn up norms aimed both at fostering the frequent and fruitful access of the faithful to the Eucharistic table and at determining the objective conditions under which communion may not be given. The care shown in promoting the faithful observance of these norms becomes a practical means of showing love for the Eucharist and for the Church.
But keep in mind that this document does contain a positive theme as well as the grim. Ecclesial communion is a relationship within the Church itself. It manifests in homes, parishes, associations, groups of friends, and most especially, across these boundaries.
To be clear, and admitting my own participation in this, the internet is often a spectacularly poor example of communion within Catholicism. Many words and actions work against outward unity and the interior cultivation of the desire for unity. Such would be contrary to church teaching as presented in the first sentence of this section. The citation of ecclesiastical norms are but one example, and not the only expression of the fostering of unity.