The concern is not with the laity serving with the bishop, but rather that the laity were serving instead of the clergy that are the ordinary ministers of Holy Communion.
In order, then, that the faithful who are in the state of grace and rightly and devoutly wish to share in the sacred meal may not be deprived of this sacramental aid and solace, Pope Paul VI has decided it opportune to authorize special ministers who will be empowered to give communion to themselves and others of the faithful, under the exact and specified conditions here listed.
I. Local Ordinaries possess the faculty enabling them to permit fit persons, each chosen by name as a special minister, in a given instance or for a set period or even permanently, to give communion to themselves and others of the faithful and to carry it to the sick residing at home:
a. **whenever no priest, deacon, or acolyte is available**;
b. whenever the same ministers are impeded from administering communion because of another pastoral ministry, ill-health, or old age;
c. whenever the number of faithful wishing to receive communion is so great that the celebration of Mass or the giving of communion outside Mass would take too long.
II. The same local Ordinaries possess the faculty of granting individual priests in the course of their ministry the power to appoint, for a given occasion, a fit person to distribute communion in cases of genuine necessity
When members of the clergy are available they should serve unless there are pastoral reasons for them not to. For instance we have a retired priest in his late 70s or early 80s that occasionally fills in for our pastor. Because of his advanced age he is concerned that he might drop the host during distribution so he “sits out” distribution. Perfectly fine with that, but the preference is that extraordinary ministers only be used when no other ordinary ministers are available. In the specific case that I presented this was was not true. There were roughly 24 ordinary ministers for a mass of approximately 250 people. Even if half of them could not serve for one reason of another there were plenty of ordinary ministers to distribute to the 250 faithful gathered there. My point was that when people see EMHCs treated with the same preference as ordinary ministers it distorts the original reasons Pope Paul VI allowed them to be named in the first place; namely only when there is great need and no other options available. I assume that is why I have never seen EMHCs used in a mass at the Vatican.
The OP mentioning that a member of the laity appeared to be assisted by a priest just strikes me as odd. If the “assisting” priest was unable to server in their own capacity then the deacon should have served and the priest and EMHC should have assisted the ordinary ministers.