The television commercial is designed to spark outrage. “Billions of taxpayer dollars spent on green energy went to jobs in foreign countries,” it intones. “The Obama administration admitted the truth — that $2.3 billion of tax credits went overseas, while millions of Americans can’t find a job. ... American taxpayers are paying to send their own jobs to foreign countries.”

But the widely broadcast anti-Obama ad, paid for by a conservative group called Americans for Prosperity, is highly misleading — a slick pastiche of untruths, half-truths and exaggerations. And it’s a prime example of what’s gone wrong with political advertising.

Who put up the $6.1 million to air the Americans for Prosperity commercial? None of your business.

That’s the problem with the independent committees gearing up to flood the airwaves with “issue ads.” Because their backers get to remain largely anonymous, they don’t seem to feel much duty to stick to the truth.

Take the green energy commercial from Americans for Prosperity. Like most political advertising, it looks and sounds authoritative. It even quotes newspaper stories to make its case.

But did $2.3 billion of tax credits go overseas? No; the $2.3-billion figure is the total size of the Energy Department’s tax credit program. About half of that money went to foreign companies or their U.S. subsidiaries, but all of it was allocated for projects to create American jobs. One of the biggest grants, for example, went to a German company — Volkswagen. But it was for a plant to build clean vehicles in Chattanooga, Tenn.

Here’s another claim from the commercial: “$1.2 billion to a solar company that’s building a plant in Mexico.” The words are technically accurate but once again misleading. That $1.2 billion — and it was in loan guarantees, not grants — went to a company called SunPower to help build a solar facility in California. The same company also built a plant in Mexico, but that was an entirely separate project, not financed by the U.S. taxpayer.

It’s true that some federal money went overseas to buy parts for wind turbines and high-efficiency bulbs for traffic lights (when U.S. manufacturers couldn’t meet the demand fast enough, the government says). But that’s not what the commercial says.

There are plenty of legitimate criticisms that can be aimed at the Obama administration’s green energy programs. I’ve made some of them myself. But doesn’t it tell you something that Republicans in Congress, led by the normally ferocious Rep. Darrell Issa, R-Calif., looked at the charges that taxpayer dollars were going overseas and never even held a hearing to air the complaints? They knew the flimsy accusation couldn’t withstand scrutiny.

That constraint doesn’t apply to Americans for Prosperity, though. It doesn’t have to answer to voters or run for reelection; its constituents are the unnamed donors that paid for the ad.

Americans for Prosperity has declared itself a tax-exempt “social welfare organization” under the Internal Revenue code, which means its official purpose is to educate the public about civic issues.

Some of the group’s backers are known. Charles and David Koch, the billionaire owners of Wichita, Kan.-based Koch Industries, were among its founders. It has four directors, including James C. Miller III, a former aide to President Ronald Reagan; and Art Pope, a former North Carolina state legislator. But they choose not to say who put up the $151 million that AFP plans to spend during the 2012 election cycle, not all of it on political advertising.

I sent messages to the Koch brothers and all four directors last week asking if they were willing to disclose their contributions. The only reply came from a Koch Industries spokeswoman, who confirmed that David Koch and his company support AFP but offered no details.

To its credit, though, the organization’s staff responded energetically — and vigorously defended every allegation in their advertising.

If money goes to Volkswagen or any other foreign company, they said, some of it probably ends up overseas, in the form of profits or managements costs. “We feel very comfortable with our message,” said Tim Phillips, AFP’s president.

Not surprisingly, he disagreed with my contention that his donors’ anonymity made it easier for the organization to play fast and loose with the facts. “The more incendiary and wild an ad is, the less credible,” he said. “We didn’t call President Obama a bad man.”

AFP isn’t the biggest of these organizations. Crossroads GPS, advised by former George W. Bush strategist Karl Rove, says it hopes to spend $300 million, along with its “super PAC” cousin, American Crossroads, which can endorse a specific candidate.

Democrats are scrambling to build super PACs and other independent committees too, but their efforts have been dwarfed by conservative successes.

This isn’t about partisanship, though. Obama’s campaign advertising has stepped over the line too. His campaign recently ran a commercial accusing Romney of sending U.S. jobs overseas when he was an executive at Bain Capital, but two of the ad’s three examples occurred after Romney left the firm.

The difference is that when a candidate’s campaign makes a spurious charge, voters can call him on it. When an independent committee makes a spurious charge, who you gonna call?

It wouldn’t be tough to solve the problem. Congress could pass a law requiring groups that wage political campaigns to identify their donors (although so far, Republicans have blocked Democrats’ efforts to do that). Or the Internal Revenue Service could crack down and yank the tax-exempt status of groups that are political action committees in flimsy disguise. But the IRS moves slowly, at least on an issue as sensitive as this.

Neither one is going to come to our rescue between now and November. Fellow voters, we’re on our own.

• McManus is a columnist for The Los Angeles Times.