Well, that was probably the case in Leningrad and maybe Moscow, but definitely not the rest of the USSR (1/6th of the world's land at that moment). And the situation was not that grave. There was even a magazine printed as blue plastic LPs called Krugozor, with rock bands. I owned a collection of many rock bands on tapes, and no one chased me for that. There was completely otherer problem - Soviet music was banned in the US, you could not buy LP of Pesnyary anywhere in the US.