The accessibility checker that you are using, which is apparently the IDI Web Accessibility Checker, is in error. It incorrectly handles the inner table (layout table) as if its cells were cells of the outer table (data table). This becomes evident if you move the inner table out of the outer table, to stand on its own after it; the document then passes the check, as it should, since layout tables are indeed allowed, under certain conditions.
Even though no repair is needed to conform to WCAG 2.0 in this respect, consider using CSS instead of a layout table, as suggested in WCAG 2.0. If the layout table is just a two-cell table, this is usually simple.