This sounded almost too crazy. After a very quick look this is what I could figure out.

Sgt. Gee was initially taken to her hometown where a funeral was held. Her family decided she should be ultimately be buried in Arlington. Transport of remains, after some point, is done by commercial flights. Not sure if that is paid for. Per DOD policy:

the primary mode of transportation will be dedicated military or military contracted aircraft if air transportation is required to further transport the deceased member from the preparing mortuary to the place selected by the PADD. All other remains requiring air transportation will be flown on commercial airlift.

A nonprofit, Honoring Our Fallen, stepped in and made a $60,000 donation *directly to the family to have her remains flown by a private flight. Given airlines' track record with moving remains, this was a blessing. The family wasn't forced to pay but, again, I'm not sure if they would have had to pay for the final commercial flight. I wouldn't be surprised if they were, though.

Everything about Zelennskyy is true.

*Edit: donation was made directly to the family, not just for the flight, see post below.