Why are there Fox brand glasses in the Oakley database?

Because they were produced for Fox by Oakley

Yep, back in September 2004, Oakley announced it acquired the license agreement for Fox and was responsible for the design, manufacture, distribution and marketing of their glasses for a period of time (to the end of the 2008 calendar year).

Thank you very much for the information. I didn't know about it

There was also a fair amount of marketing material that closely aligned with Oakley at the time. Many of the lens colors and frames matched and, in fact, the gradient lens first appeared there before moving to Oakley's main lineup.