It helps to separate two things that often get blurred: the requirement to provide fall protection, and the requirement to have a written fall protection plan. They're not the same.
Providing fall protection is broad. In construction, the obligation to protect workers from falls generally kicks in at six feet above a lower level, through guardrails, personal fall arrest systems, or other means depending on the work.
A written fall protection plan is narrower and situational. It's specifically required when conventional fall protection isn't feasible or would create a greater hazard, and you're relying on alternatives — such as a controlled-access zone or a safety-monitoring system. In those cases the standard requires the plan to be in writing, site-specific, and kept current.
So the honest answer to "do I need fall protection documentation" is: you likely need fall protection, and whether you need a written plan depends on how you're providing it. That's exactly the kind of it-depends-on-your-situation question the readiness check is built to sort out.