OP - Don't get sucked into airline jargon. It is irrelevant.

Each passenger travels on a single ticket and each ticket has its own contract and each contract provides for the circumstances under which DL will provide a voucher for the hotel or a travel credit of up to $100 per passenger (not sure where the reimbursement stuff comes from, that is old stuff from the past and from people who did not read the COC).

PNR's are an administrative fiction and the LGA agents and Red Coats could, of course, have determined your original routing, but simply did not bother or bothered, but did not want to argue because they did not have access to hotels.

At this point, each passenger will need to submit the relevant information, noting the reason for the delay, the fact that no voucher was issued and requesting a reimbursement of the hotel expense (but understanding that under the contract that the passenger agreed to, there is no reimbursement, only a $100 travel credit).

These are best handled through the web form as it gets the materials into the database faster, but you are free to submit in other manners as well.