well here are the laws in the Bahamas on ESTABLISHMENT OF PATERNITY (how they are different than the USA I don't know)
http://laws.bahamas.gov.bs/Statutes/statute_CHAPTER_130.html
>>>(2) Where circumstances exist that give rise to presumptions of paternity in respect of more than one father, no presumption shall be made as to paternity.>>>
It says that if the mother and father agree that he is the father, he is presumed to be the father. BUT, here is this little tidbit above. So, I would think that the situation we have is 'given rise'. It seems that Birkhead's attorney's would need to contract for a Bahamian attorney to file a paternity suit IN THE BAHAMAS. Why this hasn't happened yet, I don't know.