No I wouldn't say that. Other problems included: too broad a definition of communist, guilt by association, the demand for loyalty oaths, and an unwillingness to take into account ideological changes over time.

However, I strongly disagree with the notion that there was no problem at all with people working for the State Department, the Army, or even in major media outlets, who actively supported, and were working towards, the violent overthrow of the US government in favor of a dictatorship of the proletariat.

If we look at the Eich situation, there were few concerns about accuracy, no guilt by association, and Eich had ample opportunity to disclaim his prior views/actions but declined to do so. So we are left with only the core question of whether or not there is something wrong with keeping avowed communists or bigots out of public positions.

Historically, one of the conservative/anti-communist gripes with McCarthy was that he left the public believing that any and all accusations of espionage within the government were baseless political smears, making it far more difficult to expose and prosecute the actual espionage going on at the time.