Alyssa Roenigk, a reporter for ESPN the Magazine who also appears on the air, primarily covering action sports like the X Games, said she had rarely given her security much thought. For years, she usually walked from venues to her hotel, even late at night. But as she began to do more television and was recognized more often, she was told by her bosses to start taking the courtesy car provided by the network.

“At first I thought I was getting special treatment, and I don’t want special treatment,” Ms. Roenigk said. “It’s not special treatment. It’s being safe.”

Jamie Little of Fox Sports, who primarily covers Nascar and other motorsports, said: “Just last week, I got on an elevator, and there were some race fans in there, and they were drinking, and it made me a little nervous. And they were kind of watching what floor I was going to, so I pressed the wrong floor. So I go to the wrong floor, get off the elevator, wait for them to go and get back on.”

In another instance, she said, she was on an airport shuttle on her way to pick up a rental car when a man approached her. She was still not sure if he was an ardent fan or something else.

“This guy turns right into me and says, ‘Hey, Jamie, so you going to so-and-so today?’ ” she recalled. “I was like, ‘Whoa, hey, well, I’m here for Nascar.’ And he kept trying to make small talk. I went down another escalator, and when I looked over, he was literally standing there staring at me, on his phone.

“That kind of stuff makes you worry,” she continued. “You want to give people the benefit of the doubt. ‘Yeah, I’m on TV; it’s not a big deal.’ But you have to watch the mannerisms, the body language, the constant following you as they try to ask questions. I tend to be overly nice to people. When weird things happen, I honestly kind of forget about it because it’s your job and I’ve got to get on a plane the next week.”