There is also the small matter of difference between calendars, depending on when and where you are talking about. Someone pedantic who tried to make an adjustment could easily choose a different date (to make it the same) and might adjust by 10,11, 12 or whatever number of days. 

23 Oct 1852 in one part of the world might have been 11th October elsewhere. So what exactly is a "birthday" anyway

Apart from that as others have observed, dates in reality very often (more often than not) vary wildly, even with intelligent, educated Doctors and Lawyers. By days, months or even many years. It is often completely inexplicable. Sometimes there are reasons (making a child a different age to get a cheaper shipping ticket, change conscription requirements, get married, to incorporate another child into a family who is not really a child. 

Sometimes people just didn't care about dates (at all)

Aubrey Blumzon

UK