The birthdate, date of issue, hair color, eye color, rating, and height all being the same would be an absolutely astronomical coincidence.
DOB: 1:365 is not astronomical (but indeed unlikely).
Issue date: 1:2 is not at all out of the question. (Having a certificate before or after the new style's introduction.)
Hair color: 1:4 is not astronomical. (Brown, Black, Blonde or Red.)
Eye color: 1:4 in not astronomical. (Brown, Green, Blue or Hazel.)
Rating: Once you are ATP rated you start with a "Flight Engineer" rating and their is no requirement to advance in rating. Many pilots only hold "Flight Engineer" their whole career.
I don't see what is so unlikely.