> The issue the heart of Citizens United v. FEC (i.e., the Federal Elections Commission) was whether a non-profit's funding of a TV special criticizing a candidate violated the Bipartisan Campaign Reform Act.
In ordinary parlance, do we say “Apple funds iOS” or do we say “Apple makes iOS?” In Citizens United the non-profit produced and sought to air a movie called Hillary: the Movie. They didn’t “fund” any candidate’s political campaign.
> I guess it's technically true that the decision doesn't allow more money to flow directly to the campaign
By “technically true” you mean “true.” “Campaign finance” laws presumably have to do with financing of campaigns. The “role of money in elections” is a different, much broader area, much of it outside the scope of campaign finance laws. (For example, consider the alleged $5 billion in free advertising the press gave Trump. Do campaign finance laws allow the government to regulate that?)
One can imagine lumping in scenarios where someone is attempting to bypass a campaign finance restriction by directing a third party to produce content for the campaign. But that’s not what Citizens United involved either. There was no allegation of any such “indirect” campaign financing. Instead, the government tried a naked power grab: punishing a non-profit for making a political movie, with no showing of any link to the campaign beyond that.