Akwat Kbrana said:

From the ROTJ screenplay:

Obi-Wan Kenobi said:

When your father left, he didn't know your mother was pregnant. Your mother and I knew he would find out eventually, but we wanted to keep you both as safe as possible, for as long as possible. So I took you to live with my brother Owen on Tatooine... and your mother took Leia to live as the daughter of Senator Ogana, on Alderaan.

Of course, how a faneditor would go about communicating all that to the viewer is another matter entirely...

Is this from the novelization? It sounds pretty close if I remember correctly, though I'm at school and don't have access to it. That could be a good explanation, though more would be required, I feel, to explain it at the end of ROTS as well.

Now that I'm thinking about their being brother and sister early on, I think this makes it clear that Leia cannot be revealed to be Luke's sister when Padme gives birth or else it would both spoil the surprise as well as gross out any potential viewers learning too early on, were we to watch it in the 4,5,1-3,6 order (we have to come up with a more concise way of describing this viewing order).

EDIT: AHA! It is a direct quote from ROTJ! I'm so good.