This sounds like it could be a communication issue. When entering the USA (assuming not preclearance) everyone goes through immigration and customs, walking all checked bags through customs. Then one typically just drops the checked bags immediately after exiting customs, assuming that the bags were checked through. Alternatively, most airports have DL agents just after the customs exit who can check the bags if needed, print boarding passes for connecting flights, etc. Worst case would be taking bags up to DL check in counter, where agent could say it's too early or there might not be an open DL counter if all DL flights depart much later, but I can't think of an international gateway in the USA where that would be an issue.