Very good, you've added another dimension to this controversy. Why would they black out the number indeed? So it can't be cross-referenced? Because it's his sister's number, perhaps? This controversy has legs.
The most entertaining theory I've heard is, they blacked it out because it's blank. Why blank? Because it says "DATE FILED BY REGISTRAR" instead of "DATE ACCEPTED BY REGISTRAR", the assumption being that a BC doesn't get a number until it's accepted. And the implication is that filed means, She said she dropped him on US soil, but we [State of Hawaii] haven't verified it!
My own theory? The doofus who posted the document had a numerical eek moment: Number! Identity theft! Better black it out! And now the Obama people are laughing at the extra controversy thereby engendered.