corp + state = fascism

My friend Joseph recently reminded me that Benito Mussolini allegedly said "Fascism should more appropriately be called Corporatism because it is a merger of state and corporate power."

In addition to the difficulty in verifying the quote (damn, there's a lot of that going around these days), there is some legitimate doubt that, when he used the word "corporatism," Mussolini meant what we mean today.  Chip Berlet, however, points out that BM used the word to describe guilds, which would imply business conglomerates. Here's il duce himself saying:

It may be objected that this program implies a return to the guilds [corporazioni]. No matter!... I therefore hope this assembly will accept the economic claims advanced by national syndicalism. (p. 24)

It doesn't ultimately matter whether BM or his ghostwriter ever said this specifically.  Fascsism is an elite-driven historical act of desperation, where the freedoms, including market freedoms, associated with capitalism are sacrificed in order to save capitalism.  It's capitalism's "special period."  In that sense, it is a merger of the state and the corporate elite, or the intensification of that already-existing relationship.

So here's the question the quote, and discussion around it, sparked for me: Why do conservatives always conclude the solution is to eliminate state power only? Does it have anything to do with their conflation of fascism and Stalinism?
A third essential element of fascism, which evolved by necessity, but whose origins were intrinsic to the goals of fascism, is the thorough, public use of brutality to crush dissent and/or deviance. That quality is not a factor in the question, but it may be in the answer.