As long as an API rejects invalid values if they are not part of an agreed list (but not enum), the same logic should apply for fields explicitly marked as enum

As long as an API rejects invalid values if they are not part of an agreed list (but not enum), the same logic should apply for fields explicitly marked as enums. HTTP headers are not meant to be a limited set. As for the HTTP methods, it's a clear recommendation from OWASP to explicitly reject methods not supported by your API. It's like converting everything not known to POST...