Kapiolani appears to be compromised.
I don't know if you remember this, but the 'letter' read by Abercrombie ultimately didn't match the 'letter' shown on the Kapiolani website...
Of course, if Barack Obama Jr. was really born in Kapi'olani, the hospital could resolve the issue by releasing even a single document from its patient records indicating that Stanley Ann Dunham was admitted as a patient there in 1961. In doing so, it would not be violating anyone's privacy rights, since Ms. Dunham is deceased, and Barack Obama's name would not appear on such a document.