Ms. Russini captioned an Instagram photo of the two of them: “Best date. Best C.E.O.”

The next month, Ms. Russini represented The Athletic at The State of the Times, an annual daylong presentation by the Times Company’s top executives and journalists about the company’s strategies and recent successes. Appearing with three colleagues to discuss the power of video, she again name-checked a certain coach.

“I did an interview with the Patriots head coach, Mike Vrabel,” she began.

The interview, she explained, was stilted and boring — so she asked him what she called a “throwaway” question, inviting Mr. Vrabel to share a pet peeve. The Patriots coach told her how much it angered him when he spotted able-bodied interlopers parked in designated handicap parking spots.

“This person who was so robotic on every single thing we were talking about in regards to the N.F.L.,” Ms. Russini said. “But when it came to real-life things, he just opened up.”

The video, she said, “went everywhere,” she said, because “everyone can relate to that.”

She also noted the coach’s vigilance about his pet peeve. “It’s insane!” Ms. Russini told the audience, describing her thoughts during the interview. “I’m like: ‘What’s wrong with this person? What is wrong with the Kraft family for hiring this man?’” she said, referring to the owners of the Patriots. “But, obviously he’s pretty good, right? Went to the Super Bowl this year.”

About two weeks later, she was in Arizona lounging with Mr. Vrabel in the hot tub in Sedona.

The next day, Ms. Russini and Mr. Vrabel both attended the N.F.L.’s annual meeting in Phoenix. On the patio of the Arizona Biltmore, she ferried drinks between the bar and an informal klatch that included Mr. Vrabel and other head coaches. According to two people who were there, she periodically stopped to sit on the arm of the sofa next to where Mr. Vrabel sat.