Many people often misunderstand where the Swastika actually came from.
Evidence exists that ornaments similar to the swastika date back to the Neolithic period. The Swastika is found primarily in cultures in modern day India and nearby locations.
It's used as a geometrical motif and sometimes as a religious symbol. Major world religions, such as Shamanism, used the Swastika.
If the symbol from the image you showed us is indeed owned by the Nazis, I believe that it was probably their original symbol. They probably decided to add to it so that it wasn't the exact same thing as what other groups were using. Later on, it was probably revised and reverted back to its true form, which is what we see today. (View the image below.)
The other thing I noticed in the image you posted, is the bird behind the symbol. The wingspan with the visible tail feathers is representative of the Nazi regime, as seen in the image below.
In my opinion, it's sickening that the Swastika carries the controversy it does. It originally started out as a beautiful thing - representational of peace and harmony, and was later twisted into the icon of the systematic murder of millions.