There is a whole body of thought about corporations existing outside of governments, anarcho-capitalism. In fact, the way I equated corporations and government relies on assumptions from this view.
You're coming around to the equating from a different angle, but it feels a bit lacking to me because corporations certainly can exert pressure on governments and asserting that corporations are reliant on governments would seem to downplay this dynamic.
Corporations that competed with governments had armies historically, trade corporations like Hansa or East Indies operated that way. So as long as they aren't fielding armies they are not competing with governments, just influencing them a bit.
In the large as to their goals, effects, and competition with each other, sure. I was talking about individual freedom, and in that context they are both capable of applying coercion to individuals.
You're coming around to the equating from a different angle, but it feels a bit lacking to me because corporations certainly can exert pressure on governments and asserting that corporations are reliant on governments would seem to downplay this dynamic.