Conservatives are up in arms about the surge of undocumented women and children coming across the border from Mexico. So great a threat is purportedly being caused by this influx that Republican members of Congress are clamoring for legislation that would allow faster deportations. Even President Obama seems to agree.

Much less urgency is being expressed about another sort of immigration crisis: the presence of a growing number of foreign-based corporations masquerading as American companies. Large-scale tax dodging by these firms does much more harm to the United States than the modest impact of those desperate Central Americans.

A recent report by the Congressional Research Service describes a new wave of companies going through a process politely known as “inversions.” What’s really happened is that these firms have renounced their U.S. “citizenship” and reincorporated themselves in tax haven countries in order to escape federal taxes.

Yet these companies go on operating as before, keeping their U.S. offices, their U.S. sales and all the other benefits of doing business here but not paying their fair share of the cost of government. They are the real illegitimate aliens.

While a few members of Congress have spoken out against this corporate treason, many adhere to the idea that the companies are blameless — that it is the supposedly oppressive tax system that is to blame. The editorialists at the Wall Street Journal, who can always be counted on to go to any length to defend corporate avarice, recently began a piece on inversions by writing: “What kind of country does this to itself?”

This is typical of the pro-corporate mindset: Big business, apparently, can do no wrong, so if a company does something controversial, it is the rest of us who are to blame.

In reality, many of the companies that have turned to inversions are not only tax dodgers; they are bad actors in other respects. Take the case of Medtronic, which is involved in the most recent re-registration deal involving a plan to merge with Covidien, a competitor in the medical devices industry that earlier turned itself into an “Irish” company.

Only a couple of weeks before the Covidien deal became public, the U.S. Justice Department announced that Medtronic would pay $9.9 million to resolve allegations under the False Claims Act that it made improper payments to physicians to get them to implant the company’s pacemakers and defibrillators in Medicare and Medicaid patients. The settlement came less than three years after Medtronic had to pay $23.5 million to resolve another False Claims Act case involving other kinds of improper inducements to physicians.

And five years before that, Medtronic paid $40 million to settle yet another kickback case. In 2010 the company had to pay $268 million to settle lawsuits claiming that defective wires in its defibrillators caused at least 13 deaths.

An even worse track record belongs to Pfizer, which attempted an inversion a couple of months ago by seeking to acquire Britain’s AstraZeneca but has backed off for now. In 2009 Pfizer agreed to pay $2.3 billion to resolve criminal and civil charges relating to the improper marketing of Bextra and three other medications. The amount was a record for a healthcare fraud settlement. John Kopchinski, a former Pfizer sales representative whose complaint helped bring about the federal investigation, told the New York Times: “The whole culture of Pfizer is driven by sales, and if you didn’t sell drugs illegally, you were not seen as a team player.”

Like Medtronic, Pfizer has had problems with questionable payments. In August 2012 the SEC announced that it had reached a $45 million settlement with the company to resolve charges that its subsidiaries, especially Wyeth, had bribed overseas doctors and other healthcare professionals to increase foreign sales.

Or take the case of Walgreen, which is reported to be planning an inversion of its own. In 2008 it had to pay $35 million to settle claims that it defrauded the federal government by improperly switching patients to different version of three prescription drugs in order to increase its reimbursements from Medicaid. Last year, the Drug Enforcement Administration announced that the giant pharmacy chain would pay a record $80 million in civil penalties to resolve charges that it failed to properly control the sales of narcotic painkillers at some of its stores.

The examples could continue. Corporations resorting to extreme measures such as foreign re-incorporations are not innocent victims. Their tax dodging is just another symptom of corporate cultures that put profit maximization above loyalty to country and adherence to the law.