Looking through the study, I found that the title is misleading. In fact, the study an in-depth review of a previous study about one species of plant in one location, showing that climate change was likely not the reason for why this one species in this one location actually showed the impacts that it did. Indeed, the PhysOrg article actually points out that the authors aren't saying that climate change doesn't influence plant shifts:
“I want to be clear that I’m not saying climate change isn’t happening or having effects,” Schwilk said. “I study it all the time. But we’re trying to have people be more explicit about describing the mechanisms and causes of plant shifts, because I suspect there may be a bias toward automatically assuming climate change as the reason.You see there? One of the two authors is explicitly saying that he does believe that climate change does influence plant-shift patterns, and that - like many good scientists - he wants to ensure that people look more closely at the interlinkages and not rely too heavily on simple models.
In short, on the social implication side, this study isn't actually one that debates the theory of global warming or even the theory of plant shift due to global warming. It is - to reiterate - a report that investigates one report about one plant species in one location. Therefore, if you see this study being cited in the future as proof against climate change not having an impact on plant species, then know that the person telling you this is feeding you a falsehood. Don't bite.
Full PloS ONE article here.