I ran into the exact same thing, a few weeks ago, and went through the same set of verification procedures... somewhat against my better judgment. No, they couldn't "verify me in public records," probably for the very reason that I have spent a lot of time keeping a really low profile...
I really DO hope decentralized exchanges gain some traction, but I guess it's quite a challenge to build consensus when people have such a wide range of perspectives on how money should be handled. In a sense, maybe that's one of the true "acid tests" of decentralized structures...