For my galleries, the alt text were also displayed instead of the captions. This happened for me with all of the scripts except for prettyPhoto. I wanted to use Nivo. I fixed it for Nivo, probably can do the same thing for Swipebox.
In the lightbox javascript find where the title is set then change dom selector to look for and use the “alt” attribute of the first child element. May need to pretty format to find, I used Firebug on Firefox for this.
For Nivo, open the javascript and find two instances of:
r.attr("title")
And replace with:
r.children().first().attr("alt")