REST API returns error messages in unexpected format

Summary

Environment

Confluence 5.8.9 or Confluence 6.1.0

Steps to Reproduce

Make a mistake in your request to a REST endpoint, Application/XML is returned:

Expected Results

Make a valid request to a REST endpoint, JSON output is the result

It is expected that errors such as 404 should also be returned in JSON.

Actual Results

XML is returned for the error:

Workaround

There is no workaround.

Note: this has been reported for Bamboo as well:
https://bitbucket.atlassian.net/browse/BB-4849