Gender is a bit of a stretch, if technically changeable. I don't know much on the subject but I would wager that the proportion of people who have changed gender is not statistically significant enough to change the 87% figure.
Identifiers are either immutable or they're not. They can't be sorta-kinda immutable.
Do we know if she took into account population migration / movement? Looking at the description it doesn't look like it, but I'd be really curious to see how that affects the stat. Or how the stat changes if the zip code is tied to the person's DOB. In that scenario it probably drops a lot, because (I'm assuming) most people are born in a hospital, and there isn't a hospital in every zip code. So to my first comment on population movement, maybe that's actually a representation of the effect of population migration / movement. Cool.
"True unique identifiers"? Is it anything like a true Scotsman? :-)
Something can be a unique identifier of someone in a given time point, and later become non-unique, or stop identifying that person.
It is hard to find good natural keys (that are immutable and unique). That is why many people recommend using artificial keys.