> you can't be; since you're obviously capable of observing them from the outside while they go on with their business

I think that's the wrong way to put it.

You can observe those thoughts much like you can observe your hand with your eyes. That does not make your hand any less part of you than those thoughts.

IMO the vast majority of the chatter in our minds are like any other involuntary process of our bodies. The difference is that we are culturally conditioned to identify with our minds and not our intestinal processes.