For anyone that runs into this problem;
After a day of troubleshooting and the Swagger support guys pointing me in the right direction, it turns out that this is currently caused by a bug within the AWS API Gateway custom authorizers.
We are currently using AWS API Gateway for managing our APIs, this includes managing all our authorization via a custom authorizer. The issue is that custom authorizers do not currently support passing through headers within the response and Swagger UI needs the Access-Control-Allow-Origin:* within the response header(s) to display the correct HTTP status code.
See this AWS thread regarding the issue (which is older than a year already):
https://forums.aws.amazon.com/thread.jspa?messageID=728839
Swagger UI discussion on same: https://github.com/swagger-api/swagger-ui/issues/3403
EDIT / UPDATE
This has since been resolved with the use of Gateway Responses. See this same forum (page 2):