As far as i know this box cannot be used as a fan box, if the scews go into the wood or not. This box was not intended to be used for fans so, so i think using other than 10/32 screws in this bow would be breaking the UL listing.And yes that is 12/3 romex now yellow, used to be white a few years ago, about 3 or 4 yrs ago i think.
The screws used for standard fixture boxes are 8/32 not 10. And suppose you mount the fan using the 8/32 holes and then you use the 3 1/2" wood screws that come with the fan to secure the fan to the framing member also. What is the problem?