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A tiny fraction of people have different chromosomes — XXX, XYY, XXY.

Yes, and people with Klinefelter's or Turner's or other such genetic abnormalities are still definitively male or female - If a 'Y' is present (XXY, XYY), it's a male. No 'Y' (X, XXX, XXXX), it's a female.

There are really only two real cases that should cause confusion in these cases: true hermaphrodites, and chimeras.

Hermaphrodites physically develop incorrectly, having both male and female reproductive parts, and the one that ends up being the main one visually may not match what their chromosomal makeup is.
A Chimera is someone who's absorbed another human into themselves, such as a twin in utero. While they are definitely male or female, with parts to match, many of their cells will have the other twin's DNA/chromosomes. So their DNA test may sometimes not match what they actually are.

That's a good summary — and it's good you added the bit about the hermaphrodites and chimeras.

It's important for everyone to know about these exceptions, before attempting to debate the issue of ‘trans-genders’. Otherwise, you will fall into a ‘gotcha’ trap.

Hermaphrodites are the only exception that really is an exception.

Chimeras have featured in several cop shows, as a plot device. Usually, it involves a serial killer, who gets away with murder, because his DNA does not match the DNA at the crime scene. The surprise ending — the perp has two sets of DNA! I guess it could be considered a trope.