I came across a different argument recently (it was a book on Kashmir/monistic Shaivism, at least 50 years old) that was ultimately making the same point that you are.
The argument was something like: If everything in the world only meaningfully existed within individual consciousness' subjective experience, than the world wouldn't make much sense. There would be no truth or objectivity. A universal mind is necessary to account for objectivity.
Well, it appears from the above that there is a presumption that 'only' the universal mind can comprehend objectively and 'only' those comprehended by it are objective; further, anything comprehended by individual is automatically subjective and 'only' subjective can be comprehended by it. Would that reflect the position of the book?
It might be more in line with science to say that objectivity is something that only exists in the subjective individual mind
What i'm inclined to believe is that the individual consciousness comprehends both - objective as well as subjective. The IC however, is not located in the brain (as the speaker in the video would have us believe), can brain-activity account for every experience accurately? Or does the same area flare up in every individual's brain on say, listening to a particular music which is equally liked but its experience is not directly explicable? Objective for me, accounts for the breadth whereas, subjective for depth. The supposition of an UC to account for the objective - in this case being external - would be to deny its existence w.r.t. innate experiences. The experience of 'i am' would be most objective individual experience (making UC=0, the position aka śūnya or UC=IC aka advaita (UC-IC=0)) but then it wouldn't account for infinite 'i am's - how do we know this, there is no evidence to the contrary. UC, then becomes the basis for countless ICs.
नारायणपरब्रह्मार्पणमस्तु ।