Merkel was acting on what she believed to be a moral imperative: that those fleeing danger have a right to asylum. All her decisions follow logically if you accept that premise. I. e. it would make no sense to make such a right dependent on the total number of refugees.
In the specific moment you're alluding to she made the decision to suspend the Dublin rules because they were clearly failing (i. e. refugees were clearly being mistreated by the Hungary regime, and the situation in Greece was deteriorating to the point where both the country and the refugees urgently needed relief). At that point, the basic right outlined above and the Dublin rules were in conflict, and human rights generally trump implementation specifics such as Dublin in these circumstances.
In any case, the Dublin convention governs the burden-sharing between nations and does not impact an individual's relation with these states, or their basic rights. That's comparable to, for example, medical care in an emergency: your insurance company may have all sorts of debt with the hospital, but the doctors are still required to treat your compound fracture.