"How should one interpret [the case] then?" Recognize that Citizen's United is _not_ about corporate personhood, and actually read what the case was about. The number of times I've heard people making snarky remarks about Citizen's United without having read anything about the case is amazing.
In the US, corporate personhood is about:
(1) Corporations having equal protection under the law as persons (ie the 14th amendment applies to corporations).
(2) Coporations having the same rights as persons to draft and enforce contracts, making them "legal entities". This is related to (3).
(3) "Person" as a concept applies to associations of people rather than just individuals; associations of individuals includes corporations. See here: [1]
None of these things were decided in Citizen's United and further, it had no legal bearing on the case law surrounding these things.
Instead Citizen's United was about whether a particular law violated the 1st Amendment. Specifically the law prohibited corporations from releasing media 60 days before an election if it could impact the results of that election by reaching 50,000 or more people in the electorate. But the 1st Amendment makes no distinction between e.g. newspaper companies and other corporations, so the majority opinion was that this law and other laws that limit speech of associations of people infringe on the 1st Amendment.
From the opinion: "If the First Amendment has any force, it prohibits Congress from fining or jailing citizens, or associations of citizens, for simply engaging in political speech."
