As previously discussed on this site, there is no such a thing as a "random infringement"; it is the act of copying that is an infringement. However, should the question end up before judge or jury, they will decide on the basis of evidence presented to them whether the author copied the press publication, or independently came up with the same wording.
Should it be found that the author did in fact copy a portion of the press publication, they still have a few defences left. Many are found in Article 15(1) itself (previously draft Article 11), including one for "very short extracts":
Member States shall provide publishers of press publications established in a Member State with the rights provided for in Article 2 and Article 3(2) of Directive 2001/29/EC for the online use of their press publications by information society service providers.
The rights provided for in the first subparagraph shall not apply to private or non-commercial uses of press publications by individual users.
The protection granted under the first subparagraph shall not apply to acts of hyperlinking.
The rights provided for in the first subparagraph shall not apply in respect of the use of individual words or very short extracts of a press publication.
Should none of these defences apply, Article 15(3) makes clear that the fair dealing defences found in the original Copyright Directive still apply, though those vary somewhat by country.