While it's always possible that someone might lie in their profile, I see no obvious giveaways that this one isn't genuine. It's not like she has a model-quality picture or something.
I can think of lots of reasons why someone like that might still be single. For one thing, once you reach that age, being single tends to become self-sustaining, as fewer people want to hook up with someone far outside their age bracket, and those people within your age bracket who are also single may have similar forces acting on themselves. And, of course, there's also exactly the behavior we're seeing here: people see that she's single and think there must be something wrong.
Also, as I understand it, people in Japan have a particularly strong tendency to see older single women as "damaged goods" somehow, leading many such women to become more desperate as they approach 30, let alone 40.
And there's the career factor to look at. Notice that she's in engineering? That's not exactly a career which encourages forming relationships. It's hard to do so in school, what with the workload and the lack of available peers, and it doesn't get any easier when you join the workforce. While I know people in engineering and science who have hooked up and married, I also know many who have not.
Of course, the person may have other baggage. To mention a particularly cynical way of looking at it, someone I once knew would say "Smart, pretty, or sane--pick any two." I think she was partly poking fun at herself with that comment, since she was certainly fine in the first two categories, and she knew it, but was definitely a bit out of spec in the third.
