Regarding immigration: I don't know if there was much selection bias as we were in the immigration queue for 10 years before being selected. The Anti-Defamation League told Bill Clinton that the situation in Russia was getting worse (1996), and he increased the annual quota of Russian Jews allowed to enter the US.
Regarding the second point: we have no more relatives in Russia, so the narrative is not meant to help anyone immigrate to the US.
As far as the story goes that Russians were equally discriminated against, and it was a case of bribery, you can take a look at my comment below of more family examples. Or you take a look at this list of Math problems that were specifically given to Jews during their admission exams into Moscow State University: http://arxiv.org/abs/1110.1556 . Thanks to @Prognosticus for sending me the link!