The 3-pin connector from the PSU is only used for monitoring of the PSU fan speed, not actually powering it. It can be put onto the case fan connector just fine (there's no real difference between the fan headers anyway, they're just labelled so that when the Asus monitoring software shows the "case fan" reading, it is reading the "case fan" header).
I have the same board though, and there really shouldn't be any problem using either of those fan headers. As long as it's not touching the copper coil thing, it shouldn't be an issue.