So, maybe not all the thoughts are really Parts.
Dissociation can be kind of close to "Dreaming," and that can come with nonsensical everything -- ever catch the thoughts you have on the edge of sleep? Mine are completely nonsensical.
Maybe it's something like that.

I also have lots of nonsensical thoughts that flow through my mind when I'm dissociating. Kind of like rotating the dial through radio stations. There's no sense to it, and it's different than when my Parts have internal dialogue.
It'll be blips of music/sounds, words/phrases/sentences - nonsensical, images, etc. no rhyme or reason.