If the animal jumps out of the vehicle, or the truck is in an accident, the animal could be injured. 
The dog only broke its leg.
The animal mentioned in the first sentence could be anything, not necessarily a dog. The first sentence says that the animal could be injured not that it broke its leg which is what the second sentence states.
exists x1 x2 x3.(n_animal(x1) & n_animal(x1) & n_truck(x3) & n_vehicle(x2) & ((exists e1.(r_out(e1) & of(e1,x2) & Actor(e1,x1) & v_jump(e1)) | exists p1 x4.(in(x3,x4) & n_accident(x4))) -> exists e2 p2.(exists e3.(Theme(e3,x1) & v_injure(e3)) & Topic(e2,p2) & Actor(e2,x1) & v_could(e2))))
exists e1 s1 x1 x2.(n_leg(x2) & of(x2,x1) & n_thing(x1) & n_dog(x1) & a_only(s1) & Manner(e1,s1) & Theme(e1,x2) & Actor(e1,x1) & v_break(e1))