"in 2000, [researcher Latanya Sweeney] showed that 87 percent of all Americans could be uniquely identified using only three bits of information: ZIP code, birthdate, and sex"
That doesn't seem right. IIRC, there are somewhere around 60,000 zipcodes. (Obviously there are under 100000.) If the population is 300 million, that's an average of about 5000 people per zipcode. Male/female splits it in half, so you have 2500 birthdates to distribute uniquely over 365 days.
Looked at another way, 365 days *times* 2 sexes *times* 60000 zipcodes totals less than 44 million. How do you uniquely ID 300 million people?
Add the problem that many people could have given you either their work or home zipcode. How does she do that?