I would share your concern but without seeing the soil it is hard to be sure.
Potatoes send lots of roots into firm soil, for food and water. But their tubers do need soft, loose material to swell in. So they will grow alright but unless you provide a soft medium for tubers as they develop, they will form on top and be green. Any extra compost or soil you can find for covering them will be good.
Thanks for your footnote, that is great news.