If you had to hire an outside company to run the Patient Protection and Affordable Care Act’s enrollment website, which would you rather have: a goody-two-shoes outfit that doesn’t know what it’s doing or a competent, well-known consulting firm that makes liberal use of offshore tax havens?

The best choice is neither, of course. Ideally, the U.S. government would set a good example and pick a skilled U.S. contractor that isn’t a poster child for clever tax shelters. Instead, the job of taking over construction of HealthCare.gov, which failed miserably when it debuted in October, is going to Accenture Plc, which switched its place of incorporation in 2009 to Ireland from Bermuda. It will replace Montreal-based CGI Group Inc., which got the blame for many of the website’s early problems.

It was only last May that the Senate Permanent Subcommittee on Investigations held hearings excoriating Apple Inc., which is based in Cupertino, California, over its use of Ireland as a tax haven. So it’s a bit surprising to see that hardly anyone is complaining about the Accenture hire. This may be an example of an orphan controversy. It’s sitting there waiting for someone to make a big deal of it, but there aren’t many politicians with an interest in doing so — even on a hot-button subject as politicized as Obamacare.

Democrats in Congress generally don’t want to be seen badmouthing the White House or the Affordable Care Act. Many Republican lawmakers (and plenty of Democrats, too) may be reluctant to criticize corporate tax dodges. For instance, Senator Rand Paul of Kentucky, a reliable Tea Party basher of Obamacare, spent much of his time at last year’s Senate hearing defending Apple’s use of offshore refuges to avoid U.S. taxes.

Accenture has endured so much criticism over the years for its use of tax havens that it even has a disclosure in its annual report warning investors to expect as much.

“Some companies that conduct substantial business in the United States but which have a parent domiciled in certain other jurisdictions have been criticized as improperly avoiding U.S. taxes or creating an unfair competitive advantage over other U.S. companies,” Accenture said. “Accenture never conducted business under a U.S. parent company and pays U.S. taxes on all of its U.S. operations. Nonetheless, we could be subject to criticism in connection with our incorporation in Ireland.”

That isn’t the whole story. Accenture got its start as part of the Chicago-based accounting firm Arthur Andersen. The firm’s consultants won an agreement in 1989 to form their own unit, Andersen Consulting, which remained affiliated with Arthur Andersen until 2000, when the two organizations severed ties. Andersen Consulting changed its name to Accenture in 2001 and went public the same year. Then, in 2002, Arthur Andersen imploded after being indicted in connection with its audit work for Enron Corp., the failed energy trader.

In other words, Accenture’s roots date back to a once-iconic American business, which helps explain why it’s gotten a lot of heat for incorporating in tax havens since spinning off.

In a 2002 report, the Government Accountability Office found that four of the 100 largest publicly traded federal contractors were incorporated in tax-haven countries. Accenture was one of them. The others were conglomerate Tyco International Ltd. and oil-services companies McDermott International Inc. and Foster Wheeler Ltd. Since then, Foster Wheeler and Tyco have switched locales to Switzerland from Bermuda. McDermott is still incorporated in Panama, while its executive offices are in Houston.

Plenty of other companies have drawn similar scrutiny. In 2008, the GAO released a report that looked at the 100 largest U.S.-based federal contractors that were publicly traded. It found that 63 of them had subsidiaries in tax havens. Citigroup Inc. had the most with 427, including 91 in Luxembourg, 90 in the Cayman Islands, 19 in Bermuda and 16 in Ireland.

All that said, if Accenture can make HealthCare.gov work properly, there probably won’t be many people criticizing it as a poor choice, model corporate citizen or not. The government doesn’t need angels for this job. It needs people who know how to build a good website.

(Jonathan Weil is a Bloomberg View columnist. Follow him on Twitter @JonathanWeil)

AFP Photo/Karen Bleier