Fiddler doesn't do anything special (by default) based on the request method.
In the scenario where the traffic isn't shown, does the request fail or succeed? If it succeeds, that implies that the request has been captured by Fiddler and it simply isn't visible. If it fails, that implies that the client is not properly using the system's proxy settings for the request in question.
Your first step should be to click Help > Troubleshoot Filters and retry the scenario to make sure that you're not capturing the traffic and just filtering it out.
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