Yes, it’s true, fascism is a system of ‘ ‘corporatism’, but the sort of ‘corporations’ they are referring to are not the sort we have today. In Mussolini’s system there were 22 (I think) corporations each representing a different industry (metallurgy, farming, textiles etc.). This system is closer to a medieval guild structure than a publicly traded corporation. These corporations then were directly controlled by the government — sort of the inverse of what we have today — corporations now control the government more or less. Ultimately it is not their economics that is particularly bad (the new deal actually took after some elements in corporatism), but their reaction to dissent and their ideals of ethnic purity.
You also have to understand that we share none of the values that come along with a fascist state — greed was not what was endorsed by the fascists, but of anti individualist submission to the state. It was explicitly anti-materialist and idealist in nature (the opposite of what we have today). Today we are hyper-individualist and internationalist. If you were to go onto an actual neo-fascist website you won’t find them supporting these policies at all. If we do happen to have a similarity here or there it is usually a superficial one.
What we have today is exactly what a Marxist would predict as the late stage of a capitalist system. Today the only thing we really share with fascists is an “anti-communist” sentiment which doesn’t necessarily denote any particular stance.
If you look at some of the principle philosophers of fascism — Giovanni Gentile in particular — you will not find that the system of today is anything at all like what they lay out.
As far as it not being old fashioned you should look at the turn of the century capitalism and see how similar things are turning out today.
I believe it’s a problem that we tend to conflate ‘bad government’ and fascism: there are many ways to poorly govern and be oppressive that are not fascist in nature.
Sorry if this is quite jumbled. I will clarify anything if asked.