I imagine there's a tight line to walk between what's illegal and legal and the ex-cop knew exactly what to say/do to get what he wanted without breaking any laws. Pretty sketchy any way you want to look at it though.
Don't understand why this guy would let anyone, be it SFPD or otherwise, take a step into his home without a warrant.
Because they said or implied they were police officers, and because they said or implied that he or his family could be deported.