The "true X" construction is semantically productive in a wide variety of contexts (a true friend, a true patriot, a true gentleman, a true villain, a true genius, a true cat...) In each case, it presupposes that some things that would normally be termed members of the class are not true ones (that not all of those who are normally labelled friends are true friends, for example). At least for animate nouns, it seems to distinguish between a broader use of a term based on appearance or convention, and a less inclusive one referring to a sort of ideal that members of the broader class may or may not live up to. Thus a true cat is one that exhibits, in exaggerated form, all the characteristics that we associate (accurately or not) with stereotypical cats; a true friend is one who exhibits the characteristics of friendship in circumstances where others would fail to exhibit them. Anyone can be a Scotsman merely by being born in Scotland, but to be a true Scotsman, you probably have to wear a kilt all the time, love haggis, roll your r's, etc.
Obviously, this feature of English is not inherently fallacious or misleading; using the phrase "true X" simply saves us the trouble of saying "an X that more than satisfies our expectations of Xs". Now that more people actually know foreigners personally rather than by report, it's become painfully obvious how far from reality most national stereotypes are, so this construction sounds rather silly when applied to Scotsmen; but even there it nonetheless conveys a fairly clear meaning to anyone familiar with English culture.
Interestingly, though, the rhetorical move originally criticised is not always misleading either. You can undeniably be a Scotsman (or a cat) without being a true Scotsman (or a true cat), so the suggestion that calling someone not a true Scotsman saves the original sweeping generalisation about Scotsmen is false. But if you're not a true friend (or a true gentleman), you're not really a friend (or a gentleman) at all - just as fool's gold isn't really gold - so calling someone not a true friend, if justifiable, does save your sweeping generalisation about friends, or, more accurately, your statement defining the characteristics of a friend. A poem I studied way back in middle school provides an entertaining example of the non-fallacious use of an (implicit) "No true Scotsman"-type argument:
Ramped and roared the lions, with horrid laughing jaws;
They bit, they glared, gave blows like beams, a wind went with their paws;
With wallowing might and stifled roar they rolled on one another,
Till all the pit with sand and mane was in a thunderous smother;
The bloody foam above the bars came whisking through the air;
Said Francis then, “Faith, gentlemen, we’re better here than there.”
De Lorge’s love o’er heard the King, a beauteous lively dame,
With smiling lips and sharp bright eyes, which always seemed the same;
She thought, The Count my lover is brave as brave can be;
He surely would do wondrous things to show his love of me;
King, ladies, lovers, all look on; the occasion is divine;
I’ll drop my glove, to prove his love; great glory will be mine.
She dropped her glove, to prove his love, then looked at him and smiled;
He bowed, and in a moment leaped among the lions wild:
The leap was quick, return was quick, he has regained his place,
Then threw the glove, but not with love, right in the lady’s face.
“By Heaven,” said Francis, “rightly done!” and he rose from where he sat;
“No love,” quoth he, “but vanity, sets love a task like that.”