I think that might indeed be a catch in some instances, but in others (at least for us) that's plenty good. Maybe in the EU people are used to seeing Italian brands at their grocery stores/supermarkets, but I suppose that for anyone outside of Europe, these small grocery shops are almost like exotic delicatessens. Give us even one grocer like this in the village we're staying in, and we feel like we're in paradise!
For La Morra, here is a screenshot of 3 grocery stores and one bakery, all on the same main street, and all with great reviews....that's plenty of options for self-catering for a three-day stay (and I am prevented from mentioning the butcher, as I'm a vegetarian...
) :
View attachment 41106