In documentation itemtypes/http the for field "Convert to JSON" states that headers will be captured in "header" key, whilst empirically testing - that is true only in case if another related field "Retrieve mode" is set to gather headers.

Proposal is to change this line:
Headers are saved as attribute and value pairs under the "header" key.
Into:
Headers are saved as attribute and value pairs under the "header" key, if "Retrieve mode" is not set to "body only"