What you control is the intentional revision of thought.
(I am acquainted with earlier studies about the corpus callosum but I do not know why you would mention that, what it would prove: maybe you could be clearer? I do not see how it could affect the notion of critical thinking.)
Not only are the rationalizations i'm talking about and which some of these papers allude to not intentional, they often happen without your conscious awareness.
I want to check the papers you proposed as soon as I will have the time: I find it difficult to believe that the conscious cannot intercept those "changes of mind" and correct them.
But please note: you are writing «Not only are ... not intentional»... Immature thought needs not to be intentional at all: it is largely spontaneous thought. But whether part of an intentional process ("let us ponder towards some goal"), or whether part of the subterranean functions, when it becomes visible (or «intercepted» as I wrote above), the trained mind looks at it with diffidence and asks questions about its foundations - intentionally, in the conscious, as a learnt process.
https://pmc.ncbi.nlm.nih.gov/articles/PMC3196841/
https://pure.uva.nl/ws/files/25987577/Split_Brain.pdf