The mark attaches to a signature
It is tempting to think of legalisation as something done to a document. It is not. Each stage looks at a mark on the page and says whether the person who made it is who they appear to be. The paper is simply what the signature happens to be sitting on, and that small shift in view explains most of what follows.
Haiti's route does not change the question
Haiti has not joined the Hague Apostille Convention, so document legalisation for Haiti runs through consular channels and ends at a desk outside Britain. A longer route means more offices reading the same page, and every one of them starts from the same place: is this a signature that a public body stands behind?
There is no finished article called an apostille issued in Birmingham for use in Haiti, so the British certificate can never be the last word here. What the British stage can do is settle the signature question cleanly, which is exactly the groundwork a consular desk expects to see already done.
Public signature or private one
A registration officer signing a certified copy of a birth entry signs for an office, and that office keeps a record of who may sign. A company director signing a letter signs for themselves. Both signatures are honest; only one of them can be checked against a national record, and that is the whole difference in practice.
This is why two papers that look equally official can behave so differently. A record from a public register moves through the chain easily. A privately signed sheet has a further problem to solve first, and solving it is a separate piece of work with its own cost and its own timetable.
Finding out what you are holding
Spend ten minutes on the sheet before spending anything else. A named office, a stated role, a reference number and a seal together tell you that a public body stands behind the mark. Their absence is not a fault in the paper; it just means the paper begins somewhere else in the chain than you assumed.
For births, marriages and deaths the shortcut is obvious. A fresh certified copy from Birmingham Register Office at Holliday Street arrives with a clean public signature already on it, which removes the question entirely and keeps the record you hold at home out of the journey.