As I mentioned in the comments earlier, Yes you can blind-fire from cover in Far Cry 3.
The tips shown in the loading screens are correct.
To do so, get behind any cover that your weapon can shoot over or shoot around. Then just simply hold down the button mapped to shoot your weapon! (By default: either
Right Trigger or
Left click depending on which console you are playing on)
Note: Be sure not to aim down your sights ! If you aim down your sights, your whole body will be exposed and vulnerable to the enemy. Also note, that while blind fire may help during hectic fire fights, bullets can still travel through some cover! So be weary of what you are using as cover.
Blind fire also works with grenades!