No, that’s not completely true.
Players from Bulgaria, Romania and Albania were not allowed to leave. Players from Russia were only allowed to leave when 30. Players from Czechoslovakia were only allowed to leave when 32. Players from Yugoslavia were allowed to leave their country when 27.
Not sure why you can’t find that information, but the information I gathered was via people in this thread, several FM researchers, friends from Slovakia, Poland and Hungary, a book on Soviet football among others.
It is a bit the same with the foreign players rules in Europe. Not having internet at that time means it never got online.