This is clearly stated on p. 549, where it says, "the determinatives that function as degree modifiers are illustrated in ," and then gives [37x] He seemed [all confused].
Note that the x in [37x] is the Roman numeral, which is to say that all is one of 10 determinatives—it's the last example—to function as a degree modifier. The category of determinatives is small, comprising 35 or so members (depending on how you count and excluding the cardinal numerals). In other words, a sizable minority of determinatives have this function. Now, you could posit adverb counterparts for each of them, as B&T do, or you could just say that this is one of a number of functions that determinatives can take on.
Of course, if you regularly fail to distinguish between category and function, you might assume that determinatives function only as determiners and overlook the generalization that a clear category-function distinction allows you to capture.
At any rate, either B&T didn't read the parts of CGEL that they cite, or perhaps they didn't understand it because they had some preconceived notion of what could function as a modifier. Or maybe the devil made them do it.
Buchstaller, I., & Traugott, E. C. (2006). The lady was al demonyak: historical aspects of Adverb all. English Language and Linguistics, 10(2), 345–370. doi:10.1017/S136067430600195X
†B&T gloss demonyak as "possessed by the devil" so al demonyak would translate so something like "all possessed" or "completely possessed".