UV filters are frequently used specifically because they offer a cheap front element that can protect a lens from damage. (That said, there is debate on if the loss of quality that can occur from using a front element is worth the protection afforded by them.) I suppose in theory it might be possible for a filter to cause damage in a fall, but they are far more likely to prevent damage and save a lens.
A fall is a very complex action and no two are ever going to be the same, but lets talk a little about some of the mechanisms involved. Glass (or any other solid material) breaks when it is deformed beyond its tensile limit (how much it can stretch). With a front element or lens, this could occur from a side impact deforming the case to the point that the case itself deforms the lens and breaks it or from a direct impact against the lens element.
If the impact is on the side of the camera, a lens filter isn't going to do just about anything to help absorb the damage as most of it will be absorbed by the case itself. It adds a little additional material to spread the force over, but the overall impact is likely going to be insignificant.
In the event of a direct impact however, it is guaranteed to reduce the energy involved in the collision with the main element. Energy can't be created or destroyed so the energy the lens picks up during the fall has to go somewhere. Similarly, both the deformation and the breaking of the front element require energy to be expended. That energy that they absorb is energy that can't subsequently go in to damaging the front element.
Now it's impossible to tell if there might be other damage as a result of the filter. It is possible that the glass from the filter might scratch the lens element (though generally front elements are hardened and should resist this.) It's also possible that a piece of glass from the element could get lodged in such a way between the ground and the lens that it could increase the concentration of force in one area, but that would simply be bad luck. Similarly, it is possible that the direction of the fall could be altered by the front element breaking in such a way that it hits a weaker part of the front element causing more damage with less energy than if the lens had not had the front element.
Those are all random freak chances though. In general, the less energy in a collision, the less damage there is likely to be. The front element will absorb a substantial amount of energy in any direct impact with the front of the lens and thus generally reduce the amount of catastrophic damage incurred, potentially tipping the balance between a scratch and a crack.
It also does prevent minor scratches and keeps dust off the lens, but these are probably insignificant next to the impact of a flat front element being added to the optical system (though it does help offset the image quality loss a little.)
Ultimately the question of if a lens filter is worth it or not as a protection measure is very debatable due to the impacts on quality and the fact things like lens hoods have a bigger impact on absorbing energy, however the fact is that much more often than not, a front filter should reduce the damage in a fall where the impact is directly on the front of the lens.