Okay, let's play devil's advocate.
You're the governor's office, and you're dealing with the response to a Cat-3/Cat-4 hurricane. You have storm surge, flooding, power outages across large swaths of area, and varying levels of devastation. Your emergency response teams are working as hard as possible to manage the situation.
You receive calls from a nursing care facility asking for help due to the situation they're in after being abandoned by staff and management of the facility.
Do you:
A. Immediately override the people in charge of search and rescue operations and retask units to go straight there and help, potentially risking other lives in more dire circumstances?
B. Do you collect information and then contact the people who are directly in charge of boots on the ground handling Search and Rescue with the information you have on their situation for them to act upon?
Also, the two things that come to mind are:
If this is the same facility that's been in the news since it happened, the place was in very close proximity to a hospital, and apparently a staff member of the care facility called the hospital requesting help directly.
There's an unknown number of calls being received by the Governor's office requesting assistance during and after the hurricane. Among how many messages and calls were these messages recorded?
This does not in any way excuse or absolve the office of any negligence they may have shown in this case. This is only meant to point out the big picture and suggest that without knowing all of the details on both sides, it's impossible to tell whether the Governor's Office acted reasonably or not.
TL;DR: Shit was going down all over, the Governor's office was likely inundated with calls and messages begging for help, and the governor's office was not directly managing the S&R efforts or emergency response. Without more information, just noting that they deleted the messages doesn't really amount to a smoking gun.