Not arguing your (solid) original point, but since we're caring about the details, I'll point out that Buckley v. Valeo (1976) ruled that spending money to influence elections is a form of constitutionally protected free speech.
Citizens United may not have stated it, but I'd say that money as speech is well established, precedent-wise. Though, sure, money spent with no intent to influence elections is probably not going to clear that bar.
Also, if anything, I'd say the popular simplification of Citizens United is that it ruled that businesses are people (meaning have personhood, rather than made up of people in the Romney sense).
I'll leave it to others to argue how correct that simplification is.