Kyushu happens to be close to the southeastern part of South Korea where Hyundai and other automakers manufacture about 1.65 million cars per years. Hyundai is beginning to use Toyota-affiliated parts suppliers from the Kyushu region, which the Japanese juggernaut sees as a growing threat from an aggressive competitor.
Toyota gets particularly miffed when suppliers sell parts that it helped jointly develop to other companies like Hyundai. In the past it let the transgression slide for competitors such as Honda and Mitsubishi because the practice resulted in lower prices on parts for Toyota itself. Apparently Toyota's would be willing to give up the discount if it means making life a littler harder for Hyundai.
Toyota no longer sees General Motors as its biggest competition, but rather the South Korean company that could. As such, Toyota is considering asking its parts suppliers not to sell to Hyundai and may resort to raising its stake in these companies in order to force them to do so.
Thanks PassingAlong for the tip!