What Esna and Morlag said. That's the main point.
For sanity's sake, if the community only accepts what can be 'proven' (which is damn little) then there is really no point to RPing. If someone says something, and if one is not sure whether their meant to be lying or grandstanding or what have you, a quick ooc, "yo duder, your character really such and such, or you just messing around." Get to the truth and run with it. Else, we can all quit RPing and just write fiction.
This depends on the group you are RPing with. Some of the friends I've played with in EVE have made up some exceedingly fantastic backstories (mine included) which would have been (and were) ridiculed if (when) they'd ever been made public -
which is part of why they never did. We kept to ourselves, we had our fun.
The more people that are going to be exposed to something, the more carefully crafted (or simply harmless) it's going to need to be to avoid a chorus of "Prove it!" The IGS is about as wide exposure as exists, and it's basically the last place you ever want to make any claim that isn't backed up by in-game action, particularly backstory stuff. I remember when Merdeneth (I think?) claimed to have set up orphanages in the Republic, and people came out of the woodwork to attack him (including some truly heinous examples of godmoding). Claiming to be the distant relative of someone famous is almost as certain a way to be mocked/questioned/discredited as actually claiming to be that person. Possibly worse, as claiming to be someone famous will get you accused of insanity, while claiming to be related with get you called a liar.
RP is built on people working from a shared understanding of the world. Yes, it would be nice if people were willing to accept background stories at face value - and many of them are. But there's a reason that the IGS is a cesspit of some of the worst RP you'll ever see. If I weren't such an RP addict, the IGS would have kept me away from EVE RP entirely. If you say anything on the IGS that is more detailed than "I am a capsuleer," someone is going to try to say that you're wrong.