If all associated attributes of an intended primary key are identical, is it still a true primary key?

I'll start with an example. If I have a person table with intended surrogate primary key Id:

+----+------+------------+-------------+
| Id | name |    DoB     |     SSN     |
+----+------+------------+-------------+
|  1 | John | 1901-01-01 | 111-11-1111 |
|  2 | Jane | 1902-02-02 | 222-22-2222 |
|  3 | John | 1901-01-01 | 111-11-1111 |
+----+------+------------+-------------+

Note Ids 1 & 3 have the same attributes; They both represent the same person. Now from what we know about the theory behind what constitutes a primary key, which I think is well summarized here : > - The primary key must uniquely identify each record. > - A record’s primary-key value can’t be null. > - The primary key-value must exist when the record is created. > - The primary key must remain stable—you can’t change the primary-key field(s). > - The primary key must be compact and contain the fewest possible attributes. Consider the first bullet, "*The primary key must uniquely identify each record.*" In my example, I suppose whether or not each Id does represent uniqueness depends on what's really supposed to be considered unique. A different database record? Yes. A different person (what the records are supposed to represent)? No. So multiple Ids represent what is functionally the same subject generating the data, present in 2 records. A "two to one Id" of sorts. I've not read anything that directly address the scenario my example illustrates, as is relates to what is or is not a PK. 1. Does this example violate the theory behind what constitutes a primary key? 2. If not, does this example illustrate a violation of any larger principles of database architecture, or can this concept be reduced to something as simple as "duplication of data - clean it up"? Many thanks.