Saying "fascist corporatism was to achieve organic national unity by putting both corporations and unions under control of the government" is disingenuous. Under fascism, the government IS the corporations. Unions only existed to prevent unionization; it's not a real union if it is controlled by the company. Fascism was not the ultimate control of corporations by the government (that's socialism), its the other way around.
Given that libertarianism (I have never seen a descriptive definition of the term leftist) is all about individualism, it should not be at all surprising that the two are treated as so similar. You are doing the reviewer a disservice by saying he conflated the two. He just said they reflect each other.
Finally, in a practical sense, libertarianism and fascism are deeply, deeply intertwined in America. Here's[1] a popular alt-right blogger saying as such, using essentially the same arguments as I am. There's also this guy[2]. Ayn Rand made an argument like yours, that fascism is statist[3], but it holds zero water and doesn't even bear strong resemblance to modern American libertarianism. Her argument is that without a state government, corporations become the state- and therefor the solution is to give the state more power, so it doesn't become fascist. So... the way to become less statist is to give the state more power. That contradiction underlies the cognitive dissonance of libertarianism. The "rules" of libertarian canon cannot exist without state enforcement, the minimization of which is the avowed purpose of libertarianism.
[1] http://therightstuff.biz/2013/01/23/fascist-libertarianism-f...