Even so, she has had her own brush with a stalker.
"He thought he had a relationship with me that wasn't happening," she says, recalling the delusional fan. "I didn't KNOW that person!"
As a past star of Asian-based action films, after which she played the title character of the CW thriller "Nikita" for four seasons, Maggie has done her best to evade off-screen attention of all kinds.
Now, in the early weeks of her new series, which airs Wednesdays at 10 p.m. EDT on CBS, she has braced for an even greater challenge to her goal of staying out of the public eye.
On "Stalker," she and Dylan McDermott star as detectives who investigate stalking incidents for the Threat Assessment Unit of the Los Angeles Police Department. Maggie hopes her series will shine a light on the trauma of being stalked, and serve as a reminder that everyone can take steps to safeguard their private lives.
"With social media today, all our lives are more accessible and on display," she observes. "There's an immediacy in our culture now, where whatever you feel at this moment enters your head and comes out your fingertips into your phone and into the world."
Unless, that is, like Maggie, you disrupt the flow.
"I'm very bad on social media," she says with a laugh. "I post nothing. I don't have Instagram, and I've never had Facebook."
She does limited tweeting to publicize her show, just as she's happy to submit to on-point interviews. But years ago, a magazine asked to shoot photos with her in her home. "I said, 'Are you kidding? No way!'"
Maggie finds celebrity worship bewildering.
"Look at the people who are in the news," she says, pointing to gossip-media royalty. "I don't find them fascinating. I think they're a bunch of idiots. But everybody's interested in their lives. I don't understand that. I never understood when it was happening to ME."
That was in Asia more than a decade ago, when, to her chagrin, she realized she had punched her way to fanzine fame as a breakout action star.
Why were celebrity rags dogging her? "I don't find MYSELF that interesting!" she says.
As she discusses that invasion during a recent interview in Manhattan, Maggie is petite but still in fighting trim in snug black slacks, leather jacket and a stylish black fedora. Now 35, she was born Margaret Denise Quigley to an American father and a Vietnamese mother, and after growing up in Hawaii with an athletic bent, she found success as a model in Hong Kong to earn money for school. (Her lifelong love of animals seemed to signal a career as a veterinarian.)
"At first, I was terrible," she admits. "I was shy. And I was unaware of using looks and sexuality to your advantage, which, at the end of the day, is what modeling is."
Her modeling career didn't last long. Jackie Chan was scouting for newcomers to appear in a new slate of younger-skewing action films he wanted to produce. He signed her.
Once again a novice in a new game, "I was absolutely terrible," Maggie declares. "I had people tell me, 'I can't believe they call you a talent,' and I couldn't disagree with them. I didn't fall in love with acting until my third film, a really bad film called 'Manhattan Midnight' (2001)."
Today, Maggie (whose credits include "Live Free or Die Hard," the recent "Divergent" and, in 2006 with Tom Cruise, "Mission Impossible: III," her first U.S. production) is widely recognized as an "action star," which, she concedes, has a pejorative ring, "like I do pushups for a living, not acting." (That said, "Stalked" distances her from the rock-'em-sock-'em genre. The job of Detective Beth Davis is to crack cases, not skulls.)
"When I started in action films," says Maggie, "the idea of action was the (Steven) Seagals and the (Jean-Claude) Van Dammes, who aren't A-list actors, not by any means. And the genre was associated with that level of acting.
"Now every A-list actor in Hollywood is doing what I've been doing for 17 years. Because, guess what? It's the funnest job, the most exciting job! Tom Cruise knows it." So does Matt Damon, she adds. "And they're real actors!"
