For starters, it's by Neal Knox, noted NRA dissident. He tried to oust the NRA leadership because they're too conciliatory.
=========== The old smith gestured to a piece of paper on the workbench and said that an order had come to him to register all of his guns.
A year or two later, the blitzkrieg rolled across the Low Countries. ===========
The Belgian Weapons Law was passed in 1933. The invasion of the Low Countries and France was in 1940. More importantly, sport and hunting weapons were not required to be registered until 1990.
========= The officer displayed a paper describing a Luger pistol, a relic of the Great War, and ordered the father to produce it. That old gun had been lost, stolen, or misplaced sometime after it had been registered, the father explained. =========
A handgun would have been a "defense weapon" under the 1933 law, and required a license issued by the local police, not just registration.
Also, while the Germans got pretty nasty about reprisals in western Europe, this wasn't until later in the war. The first year or so, they tried to avoid fomenting resistance by being too hard-handed. Gunning down an entire family in 1940? Didn't happen.
In the Low Countries, Nazi repression didn't get seriously underway until 1942, when the deportation to Germany of forced laborers resulted in the first stirrings of active resistance. Even so, atrocities like the one described didn't start happening until the summer of 1943.
For that matter, this kind of inspection wouldn't have been carried out by "a squad of SS troops." More likely, it would have been done by Ordnungspolizei. And yes, somebody in his late teens at the time--as Cpl. DeNaer supposedly was--would have known the difference.
Here's a quote (translated into english) from the diaries of Paul Struye, who during the war was the chief editor of the the underground newspaper La Libre Belgique ("Free Belgium"):
========== During the first months there was truly no hostility to be detected between the population and the army. It was a pleasant surprise for the Belgians to see the German soldiers, correct in their deportment, in their attitude. They had nothing in common with the imperial troops of 1914-1918. Belgium was occupied by an army in which order and discipline ruled, without atrocities. ==========
Source:
Another thing to bear in mind is that the Germans need not have gained their information from Belgian government records. Collaborators ratted on their neighbors in every occupied country, and the Flemish-speaking part of Belgium in particular had a comparatively high number of them. All it would have taken was one neighbor holding a grudge who remembered from before the war that the father had this old German pistol...
Basically, this story is too full of holes to be credible. It's very moving, yes; it's designed to be, because it's propaganda.