The title of this pic is just a reverse swastika. I recall reading somewhere that if it was reversed, it meant something different, but wiki said it was a swastika regardless of direction. Does it qualify for the tag, then?

Imho, nothing wrong with tagging it for what it is; post #199528 also features a reverse swastika.

Besides, reverse or not, the swastika is associated with much more than just nazism. Plus, there's the nazi tag to help make the distinction if need be.

Yeah, the reverse swastika's been around way before there was Nazism.
In Japanese Buddhism the reverse swastika is refered to as a manji which is used as a symbolical character for eternality and balance.

I guess it could be tagged as a manji or Dharma symbol since it has other differnt names in many asian religions.