Singular "their" and deep anaphors

On Language Log today, the linguist Geoffrey Pullum posted an interesting question that's worth pondering (my boldfacing below is simply to highlight a separate, interesting observation):

Compare the following two sentences:

1. Do not speak to the driver or distract their attention without good cause.
2. *Do not speak to the king or distract their attention without good cause.

Example 1 is closely modeled on a sign found behind the driver's cab on route 29 Lothian Buses in Edinburgh. It is clearly grammatical and acceptable. (Prescriptivists might object to it, but as you know, singular antecedents for forms of the pronoun they are attested in the finest English authors since Middle English times; the prescriptivists just haven't paid attention to the evidence of literary usage.) Example 2 contrasts in only one word, yet is clearly ungrammatical (or strikingly unacceptable at the very least). Why? What is the difference between driver and king that is responsible for the contrast?

My gut sense is that this is a similar situation to the one highlighted in a paper entitled "Comprehending Conceptual Anaphors" (Gernsbacher, 1991, in the journal Language and Cognitive Processes; large PDF link) by psychologist Morton Gernsbacher about what she called conceptual anaphors, which are illustrated nicely by the sentences, I think I'll order a frozen margarita. I just love them. Gernsbacher argued that a pronoun like this is not, strictly speaking, referring to the word margarita in the first sentence, but is instead referring to the concept of margaritas. In this case, it's a so-called deep anaphor because it finds its referent not in the surface form (that is, the words themselves) of an utterance, but in the meaning of an utterance. I think that the driver example posted by Pullum is nearly analogous to the margarita example. Consider the following variant of the king example that doesn't sound too bad to my ears:

George W. Bush acts like a king, but at least most of them haven't seemed so childish.

How does that sound to you? Using king so that it refers to a class rather than an individual seems to make all the difference. I think in Pullum's driver example, the sign is meant to be able to refer to any driver who happens to be present, whereas in the king example the referent of king is a particular person.

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