On parenthetical necessities

Sydney Shoemaker reviews Tim Bayne's book The Unity of Consciousness. It's great that one of the giants of analytic philosophy is still active! (I never met him in person.) I was puzzled by one of Schoemaker's comments:

"He [Bayne] offers a "mereological" account of phenomenal unity. For phenomenal states to be unified is for them to be parts of, or subsumed by, a larger phenomenal state. And he defends the view, the "Unity Thesis," that "Necessarily, for any conscious subject of the conscious experience (S) and any time (t), the simultaneous conscious states that S has at t will be subsumed by a single conscious state -- that subject's total conscious state" (p. 16). He says that the main evidence for this view is provided by introspection. In the first part of the book he takes the subject of conscious states to be a human being. Where this is assumed, the unity thesis is clearly empirical rather than a priori (despite the "necessarily" in his formulation of it), and a good deal of the book is devoted to answering empirical challenges to it."

I am puzzled by Schoemaker's parenthesis here. Bayne's use of "necessarily" in his definition (or baptism) is, I think, entirely unconnected to the evidential sources (or not) of the unity thesis. It ("necessarily") is telling us something about the modal status of  the definition (and, perhaps, how the different parts within it are related). I thought that 'we' had learned that even empirical claims...aum...could be necessary in this sense.