The part that confuses me is who was going to kill Strauss if he didn't talk in code? If the author is going to say he followed the lead of the ancient philosophers, shouldn't he attempt to show that he faced the same threats that they did, which would cause him to adopt the same approach?
He would be denied tenure and black-listed by the publishers in the name of political correctness? This would be a form of death for a political thinker.
Given what Strauss lived through in the twentieth century, do you have to ask? He did see two world wars and the rise of Nazism in Germany. The Russian Revolution and the Cold War also occured during his lifetime. A thinker arriving in mid-century America from Europe would naturally be grateful for freedom, but also have some suspicion about the degree of tolerance that was really allowed here. Many an emigre was troubled by the political conflicts of the 1940s and 1950s here in the US. And it appears that for Straussians the fate of Socrates is always contemporary and always a threat to real thinkers.
The ambivalence in Strauss and his followers may have much to do with the contrast between the disillusioned, pessimistic European and the modestly hopeful emigrant who wanted to believe in his new country. And a common fate of the emigre was to see his intellectual world destroyed on his own continent, and threatened by commercialism and industrialization in the New World. Strauss wasn't hostile to America, but something of that ambivalence remained. More than anything else though, the comments of the Straussians themselves about their teacher and teaching fuel the controversy. Promoting the idea of an inner, esoteric teaching was a marvellous way to keep Strauss forever alive, but it has made many mistrust him.
The suggestion in the article seemed to be that Strauss himself felt that his ideas were too dangerous or esoteric for the common man so he wrote in code to let that common man think he understood but did not.