How Can I install a 4inch ceiling fan in a 3 inch hole?
I measured the “universal cross bar” so the flaps were at the right distance for my fan mount. 
I then realized I could screw the universal cross bar into the smaller ceiling mount. 

I then screwed the fan mount into the “flaps” of the crossbar (which is pretty flush with the ceiling) and into the ceiling. 

Even though there is “nothing on the other side” of the flaps, when I screwed the fan mount into the “flaps” of the “universal cross bar” - it does not appear that the fan will rip out of the ceiling. 

I think the reason the fan doesn’t rip out of the ceiling is because the screw that went into the flap is a pretty tight fit