I believe that, despite the participation in the Schengen program, they have the right to do random checks at borders - let it be people arriving by car, train or air.

Last year there was focus from the media, that a high percentage of the arriving passengers on board a certain Easyjet flight from Italy came with the intention of seeking asylum (something they should otherwise do in the first EU country they arrive in). As I recall, it surfaced that the Danish police did not do as many of these spot checks as they were supposed to do.