Well, I hesitate to take issue with the Cambridge Grammar of English, but in my experience it is simply untrue that "ordinary speakers" consider this to be standard English. Some do, but by no means a large enough proportion to make such usage "standard". It is a common error, but the implication that most people use "I" as a final coordinate while a few die-hard prescriptivists call foul simply doesn't square with my experience. It is certainly not a feature of formal English (although it is a feature of people attempting to emulate formal English, which is a different thing).
True, there is no reason that the rules of "case assignment" (insofar as English can be said to have cases in any meaningful sense of the term) cannot differentiate between a coordinated and a non-coordinated pronoun, but neither is there any reason why they should.
Another point is that English Arguer's friend insists that "Rachael and me" is always wrong, wherever it comes in the sentence. Cambridge certainly isn't saying that -- it's merely talking about possible varieties of standard English.
There is, I think, a fine line between describing the way language is actually used, and propogating badly-taught or badly-remembered grammar rules. In my experience (and that of everyone else who has posted to this thread), this falls quite clearly in the latter category.
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