The echo of the Sermon at the Temple continues in 3 Nephi 18 with the sacrament of bread and wine. Remember that Christ told his disciples that they would "minister" to others in connection with food, drink and clothing during the Sermon at the Temple. In 3 Nephi 17 we saw angels (= priests) "minister" to the children, "encircling" (dressing) them. Here the disciples distribute the bread and wine after Christ blesses it, an act again described as "ministering."
1. The fact that in chapters 17 and 18 the disciples minister in the distribution of bread and wine and "angels" minister in the encircling with garments of glory ("fire") tends to support my inference that Christ's aside to his disciples in 3 Nephi 13 indicates not that only disciples are subject to the food, drink and clothing portion of the ordinance, but that they are being trained to minister in it to others.
2. This consistency strengthens my perception that we are reading in chapters 17ff a sort of repeat, or retelling, of the ordinance.