Just because two (or even more) records agree on a fact or a date, it does not mean they are correct. It just means they contain the same information. It could still be incorrect, especially if it has been years since the event which the documents talk about took place.
A death certificate, a tombstone, and an obituary may all provide the same date of birth. The reason most likely is because the informant was the same person.
And doctors even give wrong dates of birth. It does happen.