More precisely, while I am falling, my velocity and consequently my momentum relative to the Earth steadily increases, which is analogous to debt because I will eventually need to restore the situation in which my momentum relative to the Earth is zero (because that is how people live their lives: at rest relative to the surface of the Earth rather than for example in orbit).
In the same way, the passenger in the airplane must eventually go back to being at rest relative to the airplane, but if the seat belt is very loose, "debt" (momentum relative to the airliner) can be accumulated before all the slack has been taken out of the seat belt.
Yes, the total amount of impulse (change in momentum caused by the environment's pushing on the person) integrated over time is the same regardless of how tight the seat belt is, but it matters whether that impulse is spread out over time or comes in one big jolt.
