I also made a mistake. Reading wpa_supplicant's license agreement, I saw the GPL in there and missed the part about it being dual licensed. However, the nice folks at EyeFi were quick to point out:
The Eye-Fi software utilizes LGPL, BSD, Apache, MIT, ZLib, IJG (Independent JPEG Group) and Boost licensed open-source components. None of these licenses require disclosure of the source code.So, I guess there's no Linux in there after all.
They also pointed out that EyeFi is acting in good faith and sharing improvements they make to open-source components that they use. This bug filing would seem to indicate that they use IwIP for their TCP/IP stack. This might be why p0f doesn't seem to be able to detect the card's OS.