I'm not even sure what word really fits there, let alone one that for which "postulating" might be called to mind by close association, other than possibly "posturing" (too few syllables? too pedestrian a word?).

Whatever may have been in an unusual amount in addition to trash-talking, I'm pretty certain it wasn't anything remotely connected to "assuming or asserting the truth, reality, or necessity of" of a hypothesis or explanation (at least as the word is normally used).

[Now, rant over, maybe my inner Usage Nazi can have a silent night.]