We know exactly what they were thinking at the time and the reasons for various decisions.

"Cuomo administration officials say the original directive came when the governor feared the hospital system would be overwhelmed and was focused on creating as much hospital space as possible."

"To be sure, incoming residents weren’t the only possible source of infection. Some homes believe a bigger contribution came from staffers and residents unaware they had the virus. And some say they would have taken on COVID-19 patients regardless of the state’s order."

And these were people that were discharged from the hospital and sent "home". That's pretty much what hospitals do all the time, push out people as soon as possible to make room for new patients (whether it is for ER beds, surgeries, or child birth). So they had only three options, none of which was good. 1) keep them in hospitals for longer and reduce COVID treatment capacity. 2) send them back to their nursing home that are setup for care but risk spreading disease. 3) send them to somewhere new that may not be setup for same level of care or be able to handle much volume and might still risk spreading disease. I honestly think this was a true no win situation for NY at the time.