I've been lurking for a while, and that has been addressed, though you might not have seen it. The HIPAA laws about patient confidentiality forbid giving out such information, or at least Kapiolani Medical Center thinks so:
"We don't have plans to do anything," said Kapiolani Medical Center spokeswoman, Claire Tong, when asked how the center plans to commemorate the soon-to-be 44th U.S. president, who, according to Obama's family and other sources, was born at that hospital on Aug. 4, 1961.
"We can't confirm or deny it even though all the information out there says he was born at Kapiolani Hospital. And that's because of the HIPA law."
I'm in the medical field, and I know that many hospitals and physicians are extreme about this, possibly beyond what they really have to do, because the penalties for violation are severe. Also, the bad publicity for HIPAA violation would be far more damaging than any prestige from being "the birthplace."
Welcome to FR! If I may give some advice intended to be of help, on FR, when you make a claim (at least in a controversial subject) it’s best to post a source for your claim as well (link, “actual” citation, etc).
For the record though, I tend to believe what you quoted was accurate; those in the medical field ARE quite paranoid about violating HIPAA, so the quote you gave sounds reasonable. A source would be nice though.