So how do we account for so bad a theory, bad even by Objectivist standards, in the very bowels of the Rand's epistemology? I suspect that the badness of the theory stems from the fact that it was devised, not to actually develop an understanding of real, practical meaning, but merely to serve a very limited polemical end of "refuting" the analytical synthetic dichotomy. In Peikoff's essay, the Objectivist theory of meaning constitutes the main argument against the ASD:
It follows [from the Objectivist theory of meaning] that there are no grounds on which to distinguish "analytic" from "synthetic" propositions. Whether one states that "A man is a rational animal," or that "A man has only two eyes" -- in both cases, the predicted characteristics are true of man and are, therefore, included in the concept "man." 
Peikoff's argument is a non sequitar. It is based on the erroneous assumption that the purpose of the analytic-synthetic dichotomy is to drive a wedge between logic from fact. I've already discussed the purpose of the ASD here and here. The ASD does not seperate logic from fact; it merely distinguishes between propositions based on empirical research and those based on analysis of meaning. Peikoff, Rand and their followers seem to be congenitally incapable of understanding this distinction. They resent attacks on rationalistic speculation (i.e., "pure reason"), perhaps because such attacks would deprive Objectivism of its chief modus operendi.
Is there a compelling reason for distinguishing between propositions based on analysis of meaning and propositions based on empirical research? Of course there is. Any philosophy which attempts to determine matters of fact by analyzing the meaning of words is clearly guilty of adopting a pernicious approach. So why not have a tool which allows us to make this distinction?
Is it possible that the ASD is misused by some philosophers? Of course it is. What tool isn't misused? I would contend that the chief abuse of the ASD is to assume that all propositions are exclusively analytic or synthetic. It seems to me that some statements can be both, depending on their source. To the extent that a statement is an expression of empirical research and testing, it is "synthetic." To the extent that it is based on little more than an analysis of meaning (i.e., definition mongering), it is analytic. Contrary to Peikoff's assertion, analytic statements can in fact contain information about reality: they may in fact be empirically true. However, if they are based only on an analysis of meaning, they have no epistemological warrant. They can't be trusted. They may be true, but until they're tested, we can't know whether they are true or false. Only when empirical evidence has been brought forward in their favor can they be entertained as viable conjectures about the matters of fact. But in that case they're no longer solely analytical. The statement "Man is a rational animal" goes from being an analytical statement (assuming it really is one) to a synthetic statement once it becomes a testable hypothesis about the real world. If it remains merely "true by definition," then one cannot rationally assume it is true "in reality." Truth is not determined by definitions or meaning. Truth is determined by observation, experimentation, and the testing of hypotheses. Once the rudiments of truth are broached and begin to illuminate the mind, meanings are brought forward to describe that truth. Meanings are not true in and of themselves, but are merely symbols used to express and relate assertions, some of which may describe matters of fact. Rand and Peikoff, with their mania for definitions and literal truth, somehow never understood this.