How much responsibility do I have for the story my work tells?

You're realizing that what you keep and what you cut is itself a kind of truth-telling. Every frame is a choice about what people will believe happened. That's more responsibility than a camera looks like it carries. This awareness is a gift, not a weight to flee. Most people never notice the power they hold to shape how others see. You do, which means you can use it with care. The same edit that can distort can also reveal, you get to decide which, again and again. Start treating each cut as a small promise about the truth. Before you finalize, ask whether the story you're telling is fair to what actually happened. That question, asked honestly, is the whole of the responsibility you're feeling.