If my neighbor Shmerel keeps kosher and otherwise appears to be observant to the best of my knowledge, then I'd be allowed to eat in his house (assuming I'm invited), eid echad ne'eman b'issurin, his "testimony" is sufficient.
Now what happens if it's not his house, but his foodservice business?
My impression (correct me otherwise?) is that when there were bakers and innkeepers (my impression is that people didn't eat out in restaurants, but would stop at inns when travelling) in the Talmud, their kashrut was self-certified.
Today, it's strongly normative for a bakery, ice cream shop, or the like to have external certification, even if owned and run by a kosher-observant Jew.
How long has that been the practice? Do we know anything else about its history?
I'm specifically not asking about matza factories or kosher slaughter, which have a long tradition of being under the town rabbi's supervision. For instance, Shulchan Aruch (Safed and Cracow, c. 1550) opens the laws of kosher slaughter with "who can perform shechitah"; by the time we reach Chochmat Adam (Vilna, c. 1800), his Chapter One begins: "the knives of a town's kosher slaughterers are the property of the town rabbi and under his control."