Yes, it is an issue, and a massive one. It's a failing of virtually all democracies and one that plays into the hands of strategists and spin doctors... a few months ago it was revealed over here in the UK that senior Labour figures were planning on setting up a website with the sole purpose of smearing Tory politicians with completely baseless attacks. I wish everyone looked into the details of nearly everything they're told and who was paying for it and why. While attacking the messenger doesn't invalidate the arguement, it does put it in context.
You don't necessarily need to look into who is influencing what in order to reject or ignore it. As I said before, the fundamental problem here is that people in the United States are stupid enough to uncritically accept points of view parroted to them Corporate Ads to begin with, but it doesn't stop there.
There's a wide variety of opinions, notions, and "facts" that citizens of the United States swear by that are completely and utterly incorrect. I see misuses of logic and information all the time, even on E. Something as basic as correlation is not causation is lost upon a large number of Americans. The effectiveness of advertisements, rhetoric, and carefully constructed symbolic speech is a testament to just how gullible we've gotten.
Campaign finance laws censored corporations in order to protect us from an influence which the backers of said law didn't think we had the mental faculties to resist. Maybe we don't at current, but I reject the notion that it's impossible to give us the tools to resist it.
You can't legislate making people look behind the facts and figures.
No, and that would defeat the point. If the citizenry isn't willing to exercise their power responsibly, do they really deserve an effective, responsible government? In a Democracy the Government reflects the opinions of the people who vote. Claiming that corruption is the reason our government fails to serve us adequately is just a nice way of denying the responsibility for the consequences of our actions.
I'm an idealist... but I temper that with pragmatism. I wish people would look harder at what they're told... but I understand they won't. Someone hears an ad on the radio just as they're parking up saying something. They want to look into who this group are, but by the time they get home they've got to cook dinner, look after the kids, get some preparation in for the next day at work and the thought just slips their mind. They remember some of what they're told but the name of the sponsor just slips their mind. They don't really worry about it. A few days later the topic comes up round the water cooler and they say something along the lines of "well I heard this ad that said...". And slowly but surely something that could be completely biased propaganda becomes a mainstream thought.
And maybe that's what it takes. Perhaps we need to have an election season where corporatist influence affect the electorate in a huge way and people are unhappy with the result. Unfortunately the only way that becomes a cathartic experience and a turning point for our country is if people see the real lesson in it instead of spouting off populace bullshit in response.
Critical thinking can be taught, the trend of ignorance and stupidity can be turned around. The problem right now is a cultural one. In America right now "going with your gut" (as our wonderful 43th president liked to say) is respected. Confidence, justified or not, is a virtue. A lot of people like simplistic explanations, black and white demarcation, and call actually due diligence dithering.
And large portions of the American electorate is incredibly anti-intellectual.
Our culture is just shit.
EDIT: I heard both NBC and Fox (and typically if they actually agree on something there's a bit of truth to it) that the transparency regulations will remain. The article you linked to mentions that much of the original legislation will be unaffected, so I am assuming that it the portions requiring accountability are in the unaffected portions of the law. Truth be told, I'm not sure if corporations are allowed to donate to third party organizations that advertise on their behalf freely as a result of this overturning, or if they're simply allowed to directly advertise themselves (I thought it was the latter from the reporting I'd heard on the matter).
Either way it doesn't change my opinion much, but the latter definitely seems preferable, as it is more transparent.