EU referendum, brexit and the aftermath

I just don't know how she can say this. The referendum was nearly 50/50, there is no evidence that the population has got more behind leaving in the following three years, so saying she speaks for the public as a whole when she patently does not needs calling out.

I didn't listen to her speech - it's too painful - but is she claiming she speaks for the public (wrong, she can't - the public are divided), or that she's trying her best to sort out something intractable for the public (good, or rather, least shit)? You could only claim the later, right?