It's not just Lae'zel. When you get this scene in multi-player mode, the character who triggered the cutscene is the one who is seen falling down, while the second-closest character is shown proudly standing. It's just that in single player mode, that's almost always Lae'zel.
Now I want to try an experiment to see what would happen if I triggered that scene with Lae'zel alone...
But if you want an in-game explanation, consider that Lae'zel's gith training made her confident and sure-footed on a flying ship. Her native Crèche K'liir is an asteroid outpost, after all.
That's a good point. Next time I start, I'll make sure I'm clicked on Lae'zel when I go up the stairs to see what happens.