Hi Jimmy,
Any chance you split that traffic by Mobile vs Desktop and then on Mobile traffic check the direct traffic by device? Sometimes it is related to a specific device or browser that is sending the wrong referral data.
I remember this Cyrus post, about Bing traffic (https traffic) showing as direct traffic. And there is also a post by Shahzad Abbas from Define Media on iOS traffic messing up with analytics reports. Maybe you can read those and have some insights.
Cheers,
Fabio