I think there is a bit of mixing up of different categories of people. You have to imagine that the majority of people in Europe arrive by boat or at the border to claim asylum. The moment they even say the word “fear”, “persecution”, or “asylum”, they have to be allowed into a procedure to have their claim examined. Most people do not have documents with them, so member states in general have specialized, trained officials who determine the origin of the person, their language, and so on.
It is for the member state to decide whether they are satisfied or not that the person is a genuine refugee. Then they grant a permit to stay, or they return the person, if possible.