The passage you're asking about is a paraphrase of something Boeing spokeswoman Julie O'Donnell said. If you follow the citation in the article, you can see exactly what she said, and when she said it.
"During the 1950s and 1960s, fatal accidents occurred about once every 200,000 flights," says Julie O’Donnell, a spokeswoman for Boeing. "Today, the worldwide safety record is more than 10 times better, with fatal accidents occurring less than once in every two million flights." [Emphasis added.]
O'Donnell is being quoted in 2014. According to the latest IATA safety fact sheet (published January 1, 2018), IATA measured a fatal accident rate of about one per 2.36 million flights in 2012, and one per 2.58 million flights in 2013. If I were rounding that down for a reporter in 2014, "less than once in every two million flights" is exactly what I'd say.
IATA counted 15 and 14 fatal accidents in 2012 and 2013, respectively. That's an average of one fatal accident every 25 days or so—just like you estimated. As @fooot pointed out in their answer, we've seen fewer fatal accidents in more recent years: an average of one every 30 days, 90 days, 40 days, and 60 days or so in 2014, 2015, 2016, and 2017, respectively.
I agree with your gut feeling that, if fatal aircraft accidents were happening at an average rate of one every 20 days, I'd be very surprised to see no fatal accidents at all last year. If fatal accidents were Poisson distributed in time, with a rate of one per 20 days, your chances of seeing no accidents in a year would be less than one in 80 million!
On the other hand, a year with no fatal large commercial passenger jet accidents is totally plausible, given the accident rate of one per 16 million flights that @fooot quotes. In 2017, that comes out to an average accident rate of less than one every 140 days—maybe a lot less, if large commercial passenger jet flights make up only a small fraction of all flights. If fatal accidents were Poisson distributed, with a rate of 1 per 140 days, your chances of seeing no fatal accidents in a year would be better than one in 14.