Gosh - glad I mentioned legalese earlier.
My personal details and those of my family can be quoted willy-nilly by me and my family. The fact that those details are held on a government-sponsored database cannot alter that fact. Neither the government nor any other organisation hold any form of copyright on my personal details or those of my family. Nor can the government or any other organisation even CLAIM to hold any such copyright - no amount of fancy legal footwork can alter that. Terms and conditions of use may only specify prohibitions which are legal in the first place. If any organisation ever tried to tell me that I had no rights over the use of my personal information, I'd sue 'em in a court of law and WIN.
In this case - genealogical data, rather than any other form of material - no copyright can possibly be held over the information in its raw state. It IS held over the manner in which the information is stored, so DON'T COPY AND PASTE. If the owners of the database can prove that a direct copy has been perpetrated, then they can successfully sue for breach of copyright. If raw data has been extracted AND THE ORGANISATION WAS NOT THE OWNER OF THAT INFORMATION IN THE FIRST PLACE, then there is no breach of copyright case to answer.
It's really simple - my name is MY name. I hereby, by the way, freely give anyone who wants to the right to reproduce it. So, if anyone comes across my name in a database, you're OK. But do retype it just to keep the profiteers off your back.
As I pointed out in my original post, there is no copyright over the basic text of the Bible - for the sake of argument, the King James Version. I can perectly legally re-type the whole thing, put it into book form and sell it. There would still be no copyright over the basic text of the Bible.
Oh, incidentally. No matter when it was gathered, data on names, birthdates, addresses and occupations is by nature in the public domain. It cannot be taken back out of the public domain.