Certain areas of neurological systems are time and volume constrained way more than others, and subjective experience doesn't really inform objective observation. For instance, see confabulation.

I agree, but I am not sure how it relates to the article's claim of us only ever doing one action, which I feel is grossly incorrect.

Are you referring to our language capabilities? Even there, I have my doubts about our capabilities in the brain (we are limited by our speech apparatus) which might be unrealized (and while so, it's going to be hard to objectively measure, though likely possible in simpler scenarios).

Do you have any pointers about any measurement of what happens in a brain when you simultaneously communicate different thoughts (thumbs up to one person, while talking on a different topic to another)?