Here's a list for some of the reasons that I believe it is a genuine struck through error:
1. The area in question is smooth. Most genuine struck through coins I've seen have a very smooth impression.
2. The design underneath is present, but not sharp. What came between the die and the coin was thin enough to allow a shadow of the design, but not sharp details.
3. There is enough metal in the struck through area that is absent from this area, that if it were damage, I would assume some of the metal would come above the surface of the field and some outwards past the normal diameter of a half dollar.
4. The item that it was struck through was large enough to cause an obstruction within the assembly of the dies and cause some of the letters of the periphery to be weakly struck.
5. The obverse is undisturbed.
The reasons that I've listed aren't the most technical or mechanical, so please correct me if I've got something wrong and feel free to add or make a rebuttal.