You have illustrated the wrong document. This document is for a freed slave. All freed slaves were required to produce such documents on demand to prove that they were not chattel slaves. I think it coincident that he was also a seaman. He would never had been thought to be a British subject liable for impressment unless he had actually appeared on the muster roll of one of His Majesties ships. British officers actually acted with some care when impressing seamen as they could be held criminally liable for impressing someone not eligible. The sailors that they impressed from American vessels were usually British born and the Naval officers were acting properly under British law. President Jefferson held that they had no such right. Your certificate was signed in 1807, the same year as the Chesapeake-Leopard affair when a British warship fired on an American warship and impressed four seamen who had deserted from the Royal Navy. One was British born and three were American born, 2 of whom were African American former slaves. The Royal Navy hanged the British born sailor in Halifax. They released the 3 American born sailors, apologized, and paid reparations. The three Americans had voluntarily enlisted into the Royal Navy.
You are quite right about the impressment of American seamen by the Royal Navy, one of the proximate causes of the War of 1812. American seamen were recognized as British born primarily by their accents, but also by identification by Officers or foremast jacks who had served with them in the Royal Navy. While the United States recognized naturalization as a means of citizenship, Britain did not. They held that those born British Subjects remained such. British seamen, especially members of the Royal Navy frequently deserted when they touched at an American port and became naturalized citizens. Many later became American seamen and even joined the United States Navy as their skills were highly prized and service aboard American men of war paid well and was considered a far superior life style to the life of a British sailor.
Sailors did carry these certificates to establish their nationality, but it did them little good until we fought a war over it. Interesting stuff, but nothing whatever to do with birth certificates and eligibility for elected office. Thanks for sharing.
You have illustrated the wrong document. This document is for a freed slave. Well spotted, but beside the point. I searched for "seaman protection papers" and that was the best I could do. In fact, there were many thousands of them created, and they were used to convince the British that the person being interviewed was an American citizen.
The point remains. Papers to prove you are a citizen did not begin in 1915. They were at least a century earlier. 
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I had also thought to use the case of James McClure who presented his proof of being born in Charleston South Carolina to John Armstrong, (Ambassador to France), but John Armstrong (an actual Constitutional Delegate) refused to accept them as proof he was a citizen.
British officers actually acted with some care when impressing seamen as they could be held criminally liable for impressing someone not eligible.
Many months ago when I was researching this in more detail, I believe I read that many natural born American citizens were also detained and impressed. Thousands, in fact. The British simply asserted the rule "Born to a British Father makes you British."
Interesting stuff, but nothing whatever to do with birth certificates and eligibility for elected office.
Evidence that paper proof of citizenship was asserted and understood during the 1790s.
You have illustrated the wrong document. This document is for a freed slave. After further reflection I wish to thank you for pointing this out. I have repeatedly attempted to inform Jeff that Freed Slaves became citizens, and were then able to pass on that citizenship to their children. I note on the document that it explicitly identifies Samuel Bedley as an AMERICAN CITIZEN.
So not only is this an example of a "Seaman Protection paper" it is further proof that I am correct about freed slaves being citizens.
This arrow will go in my quiver.