According to this article, Barack and Michelle Obama are completely familiar with and accepting of Kezias version of the family history.
Kezia would presumably be able to testify as to exactly what she meant by the word married in the article and whether any legal documentation might exist.
From the Daily Mail January 6, 2008 here is Kezia talking about Barack Sr:
"Barack was also worried about what his father would think because I was so young, but he gave us his approval. He sent my mother and father 14 cows for my dowry.
"Barack's father was only a cook so it was a big sacrifice. Very soon after, we were married."
That was January 1957. Kezia and Barack Snr set up home in Jericho, a section of Nairobi created for government employees, and began a family.
First son Roy was born in March 1958. Kezia insisted: "Barack was a good husband."
Read more: http://www.dailymail.co.uk/news/article-506338/Barack-Obamas-stepmother-living-Bracknell-reveals-close-bond---mother.html#ixzz0Sve7yUPO
An unrecognized legal claim with no legal record, versus a recognized legal claim with a legal record.
Hearsay versus law.