It doesn't say "the Pastor's or the Parents' responsibility"...
If the Pastor enrolls these children in the sacrament knowing that there will not be support from the parents, he is violating the directives of the catechism.
You said:
" It doesn't say "the Pastor's or the Parents' responsibility"..."
WRONG.... It does say it, but you obviously have not read the Catechism or you would have known this.
Try this on:
"2252
Parents have the first responsibility for the education of their children in the faith, prayer, and all the virtues. They have the duty to provide as far as possible for the physical and spiritual needs of their children."
Let me know if you find the other references.
Sonar5