EO also used US Weekly to confirm the end of her engagement: http://m.usmagazine.com/celebrity-news/news/elizabeth-olsen-boyd-holbrook-split-break-off-engagement-details-2015191

And the May 2015 "hooking up" article was not the result of pap pics as they had not been photographed together prior to that article, nor had it been suggested in any mainstream media outlet that they were together. So it was not perhaps an entirely unreasonable assumption that she and TH were in some way involved and that the story came from one of them (probably her) to forestall any future suggestion that he had caused her breakup and/or to get the news out there before someone spotted them and made it a big splash.

And no I don't personally think they are using their relationship for PR for the movie. If there is a relationship and if the first story came from them I imagine it was done with the hope to control the gossip by getting there first.