I know I've criticized Katy Tur on this site

[Bev54]

13. This is from an article in the WaPo some years ago about the family and there is this quote

Some years later, a magazine fact-checker called my Senate office with a deadline crisis. A story about our family was going to press, and the fact-checker was confused. She’d read about Neilia and Naomi and the accident, but when Beau and Hunt had been asked about their “stepmom,” Jill, they’d said, “Oh, no. We don’t have a stepmom.”
Beau and Hunter had long since made their choice: Jill was Mom.

The boys chose her as Mom, I doubt anyone felt it necessary to go through the legal step of adoption.