As for NASA papers and such... I have no idea. If I were running a company I'd be able to ask a lawyer; as it stands, I'm taking the risk that the SQLite authors don't sue.
Making your work public domain is not "giving up your rights". It would be the exact opposite: practicing your right to transfer your IP. Being able to transfer or sell your IP would be an important right.
Similar to physical property: being able to sell it or to give it to the public is an important right. (Okay, you probably can't give your American land to everyone in the world, but only for practical reasons, and not for some fundamental reason like that would be "giving away your rights". No, that would be the opposite: your land, you do whatever you want with it.)
As for NASA papers and such... I have no idea. If I were running a company I'd be able to ask a lawyer; as it stands, I'm taking the risk that the SQLite authors don't sue.