It would be apparent and obvious that German aircraft would be shot down over both the North Sea and the English Channel and the Luftwaffe were quite within their rights to provide a search and rescue service to assist downed aircrew that had been shot down over water and were in need of rescue and be taken back to Germany. 

This rescue service was inaugurated during the early part of the war and the Luftwaffe used Heinkel He59 and Dornier Do18 float planes for this purpose. The operated from bases in Norway, Denmark, Belgium and all along the French coast. According to RAF intelligence, these aircraft, painted white with numerous red crosses painted on them, often carried armament and were observed shadowing or being used for the purpose of observation in guiding formations of bombers to shipping targets. On a number of occasions these search and rescue aircraft were observed circling above a number of British convoys for no apparent reason. The RAF was forced to issue the following communiqué: 

Enemy aircraft bearing civil markings and marked with the Red Cross have recently flown over British ships at sea and in the vicinity of the British coast, and they are being employed for purposes which His Majesty's Government cannot regard as being consistent with the privileges generally accorded to the Red Cross. 
His Majesty's Government desire to accord to ambulance aircraft reasonable facilities for the transportation of the sick and wounded, in accordance with the Red Cross Convention, and aircraft engaged in the direct evacuation of the sick and wounded will be respected, provided that they comply with the relevant provisions of the Convention. 
His Majesty's Government are unable, however, to grant immunity to such aircraft flying over areas in which operations are in progress on land or at sea, or approaching British or Allied territory, or territory in British occupation, or British or Allied ships. 
Ambulance aircraft which do not comply with the above requirements will do so at their own risk and peril. 
Communiqué issued by the Royal Air Force July 14th 1940

When the RAF realized that the German search and rescue aircraft were posing a threat to allied shipping convoys and the armament carried was for the purpose of attack and not purely for defence, it issued orders that such aircraft would be shot down.