No time to watch the vid clip at the moment as I need to head back to work, will check it out later, but looks totally plausible, the Bug was commisioned by Hitler and designed by Porsche, Volkswagen litterally means Peoples Car.
Correct, the Volkswagen ("People's Car") was developed by Dr. Ferdinand Porsche, with Hitler's blessing, ostensibly to provide every German family with a car (previously, cars were owned primarily by a wealthy minority), but it really turned into another swindle, as the money withheld from everyone's paychecks was put towards armaments manufacture (see Shirer, Rise and Fall of the Third Reich).
The car was used by the military, and if I'm not mistaken, the Kuebelwagen and Schwimmwagen were both based on the same chassis.
The photo could be real, but we need a Bug expert. The origial issue VW had two rear windows, which formed a horizontal oval shape. This was replaced in later models, when the Kaefer (Beetle) was revived after the war. We can't see much of the rear window, but the little bit I can see does look a little like the oval.
However, I'm not sure about the reflectors/running lights on the front fenders. I don't think they were on the original Bug or added after the war.