Time, actually Rav Ovadia accepted them as Jewish and even allowed an Ethiopian girl to marry a cohen based on Responsa Radbaz 7:5 and 4:1290. The Chief Rabbinate decided to require giur l’chumra (no beracha) because of lack of documentary evidence for the time since. Declaring them safek goyim would also remove the possibility of mamzerut as their gerushin is not halachic (neither is their kiddushin so according to Rav Moshe it would not matter). Being that their practices are not in line with normative Judaism in general they do not fit my statement.
Neville, there was only an advantage to be gained by lying when they requested exit visas and help from HIAS. Once settled in America there was no longer a need to pretend.
Igor, not only Russians. Now because of cultural assimilation it is not so true. However, in my generation (I am 64) it was pretty to easy to tell if someone was Jewish. In fact, in NYC one could also tell if someone was Irish or Italian.