Those aren't words you quoted initially. So appealing to words you didn't quote to try to salvage the misleading nature of your partial original quote illustrates my point.
Your original words:
Obama wrote, “Unlike my mum, Ruth has all the documents needed to prove who Mark’s father was.” Then what’s that thing on the White House website?
Saying "Obama wrote" without noting he was quoting Auma makes it look like "Unlike my Mum" are Obama's words about his mother when they are not.
Making reference to the WH posting implies that there's some contradiction between that document and "Unlike my Mum, Ruth has all the documents need to prove who Mark's father was" when they refer to documentation for two different persons. The "documents" in the quote refers to documents to which would support Auma's claim of BHO's paternity. The WH posting proves the paternity of BHO Sr. to Obama Jr. Different things.
I quote what Obama wrote.
You claim what Obama wrote is false.