I don't recall hearing the OP mentioning that this child NEEDS food more often. You've noted the child eats well at your meals and the parent feels the child needs more food and that at home the child if fed every 70 minutes. But, unless this child is showing you obvious signs of being distressed from hunger then I don't think there is anything more to do than to tell the parent they can provide some healthy snacks for you to store should the child appear to be hungry between meals provided but that your observations have been that the child is happily playing and is eating well at the table.

Should the child be showing signs of hunger you can decide whether or not YOU want to accommodate or be firm on your current practices. There is nothing wrong with saying it is not an option in your care. Most home providers and surely daycare centers would not be considering this parent request (especially without the child showing signs of hunger).