If you use the border option, no border shows up. E.g. on Wikipedia
[[Image:Flag of Japan.svg|22px|border]]
The output is in an anchor tag: <a... class=image...><img ...image spec.../></a>.
Class "image" doesn't seem to be defined anywhere (not in standard main.css, Mediawiki:Common.css nor Mediawiki:Monobook.css). I'm not sure what CSS will generate a border in an anchor tag with an image - nothing I experimented with would work.
Other options with a frame (e.g. thumb) creates <div>s to form borders.