Going to play devil's advocate: the epigenome is changed in methylation, as explained in the article, and for a NYTimes article title, "changes our DNA" is going to be much more comprehensible to the general public than "changes our epigenome". "Tweaked" is actually a very good word for what happens--none of the base pairs are rewritten, but epigenetic changes can significantly affect the organism, even to the point of being passed on to offspring.[1]

1. https://en.wikipedia.org/wiki/Transgenerational_epigenetics