I think that you might mean KE007, not JL007. It was a regular service JFK-ANC-GMP which strayed into Soviet airspace and was shot down by the Soviet military, not the Chinese.
JL007 appears to also have a history, but related to 787 tech issues.
I don't think there is any evidence that MH370 encountered a fate like KE007, and in any case, the airspace in that region is open and constantly covered with commercial jets. While there are some political tensions surrounding islands in the nearby South China Sea (or Eastern Sea if you're Vietnamese), it's not the Cold War any more.