Here's what's wrong with your recommendation:
1. An AJAX REST API request doesn't necessarily mean "application/json". It could also be "application/x-www-form-urlencoded", which won't necessarily trigger a pre-flight request.
2. Your advice goes into detail on an aspect that is not the crux of this particular vulnerability ("Access-Control-Allow-Origin") but not on the aspects that are:
2a. How to handle the pre-flight request, which is the thing that would actually block wrong-site requests.
2b. If you're relying on a Content-Type of "application/json" to trigger a pre-flight request, then it should be made clear that this is now a security check -- it's common for server code to ignore the Content-Type header as long as the body is valid.