According to Wikipedia, the original example of the alleged fallacy was the following:
Imagine Hamish McDonald, a Scotsman, sitting down with his Glasgow Morning Herald and seeing an article about how the "Brighton Sex Maniac Strikes Again." Hamish is shocked and declares that "No Scotsman would do such a thing." The next day he sits down to read his Glasgow Morning Herald again and this time finds an article about an Aberdeen man whose brutal actions make the Brighton sex maniac seem almost gentlemanly. This fact shows that Hamish was wrong in his opinion but is he going to admit this? Not likely. This time he says, "No true Scotsman would do such a thing." —Antony Flew, Thinking About Thinking: Do I sincerely want to be right?Another common example involves trivial actions, like putting sugar on oatmeal. Later, we'll see why such examples miss the point.
In this post, I will use a non-trivial example that doesn't involve Scotsmen: "No true scientist falsifies data". The sentence rings true, but I know some scientists have falsified data. Thus, I would never say, "No scientist falsifies data" but have no problem saying, "No true scientist falsifies data". That's because the two sentences are not synonymous.
Being a scientist has an important ethical dimension. Here's the key point: we often use the word "true" to highlight the moral aspect of group membership. A "true scientist" is someone who sees science as more than a career, someone who understands the ethics of science and does their best to follow them. To Hamish McDonald, being a Scotsman implies behaving in a certain way, which includes not committing horrendous sex crimes. Someone who lives in Scotland and commits such crimes may be a Scotsman, but to Hamish, he is not a true Scotsman. We now understand why the oatmeal example is silly -- putting sugar on oatmeal has no moral significance that I can see.
Like any refinement of the subject of discussion, the word "true" may be used to avoid difficult or unpleasant conclusions or to win at all costs. But it is not intrinsically fallacious.