I agree it's possible to distract yourself with your inner monologue, but I wouldn't say it's due to the volume of your inner voice.
I liken it to people who claim they can visualise a photorealistic image right in front of them, superimposed over the real world (yes, I've met such people). If you ask them to visualize a black box that grows to take up the entirety of their vision, blocking everything else out, they have to admit that they can't do that. Because while they've identified what they're experiencing as "vision", it's not that. It's something else that kind of feels like vision, but they lack the language to articulate it.