I wouldn't draw that conclusion.
Americans are probably more likely to shoot someone with a gun when they have one but I would be hesitant to estimate how much more likely.
I would think it's mostly because of Germany's restrictions on the types of guns you can get and the laws around carrying them.
The US has more guns than people and (from personal anecdotes) gun owners typically own more than one gun. From what I've seen in Germany people who do own guns also own more than one. I know people in Germany who own a few different rifles and shotguns depending on what they're hunting. In the US it's that plus semi-auto rifles and handguns.