There is a seminal paper showing how carelessly adopting this point of view can lead to disasters: "87% of the U.S. population is uniquely identified by date of birth, gender, postal code" [1]

In many other cases, as pointed out, it's just not possible. I'm studying mobility patterns through cellphone metadata. Even if you strip out the actual phone number with a random ID you still know where a person is going, and thus re-identify them if you have other public data.

[1] https://en.wikipedia.org/wiki/Latanya_Sweeney

full name + date of birth + place of birth.

That leaves about 500 non unique individuals in a country of > 50 million inhabitants.

The very depressing opposite conclusion was discovered in the late 70's:

DE Denning, PJ Denning, M Schwartz, ‘‘The tracker: a threat to statistical database security’’, in ACM Transactions on Database Systems v 4 no 1 (1979) pp 76–96

A general tracker can always be found, unless the data released is extremely restricted. Almost anything is personally identifiable as it can be used to build a tracker into the database.

I am aware of this result from chapter 9 of Security Engineering (http://www.cl.cam.ac.uk/~rja14/book.html) by Ross Anderson, if you are more generally interested.

They actually usually cannot, especially if you want to still be able to do research into them (which is the motivation behind differential privacy).