The headline is correct, but the story gets it wrong.
You're right so many people get it wrong. I remember back in late 1999 trying to convince my coworkers that the 21st Century wouldn't begin until January 1, 2001. I even showed them an original front page newspaper that I have from January 1, 1901 that had a headline that read "Welcome to the 20th Century." Did no good.
I remember explaining to someone that the 21st century would begin on January 1st 2001, and his reaction was, “Then that Y2K problem won’t hit until 2001, right?”
Well, it all depends on what you use as the beginning of AD, no? Since I believe it started at 0 AD, then the second century started exactly 100 years later - January 1, 100 AD. It makes no sense that the first century began on 1 AD, does it? But that appears to be how you and others are accounting for time.