Judging from the Manhattan prosecutors' case against 49 Russian diplomats who allegedly defrauded Medicaid for about $1.5 million, Republicans have some salient criticisms of the government-run health-care system. What better proof of laxity and poor administration than a bunch of middle-class Russian citizens receiving, year after year, tens of thousands of dollars meant for poor Americans?

At issue are Medicaid benefits to cover the cost of a child's birth. Prosecutors say the wives of Russian diplomats filed "Access NY Healthcare" applications to receive the benefits. FBI special agent Jeremy Robertson noted that "of the 63 births to Russian diplomats and their spouses in New York City between the years 2004 and 2013, 58 of those families, or 92 percent, were paid for by Medicaid benefits." None of the families was eligible for them: Only U.S. citizens are, and even the children of diplomats born on U.S. soil retain the citizenship of their home countries.

Apart from lying about their children's nationality, the diplomatic families allegedly misstated their incomes, in most cases claiming they made less than $3,000 per month while in fact an income of more than $5,000 a month was common. That's not much for New York City, but adequate considering that diplomats do not pay for housing and other costs such as trips home.

Russian diplomats are not normally issued health insurance, former foreign ministry employee Alexander Baunov told me. An embassy usually has a medical center where all diplomats and staff are treated, and when the embassy doctors cannot handle a case, the Russian government will cover all or part of the employee's expenses at a local clinic. Getting full reimbursement may be tricky. "I was treated for an ulcer and got partial compensation, at state-owned hospital rates," Baunov, who worked at the same level as the defendants, recalled.

For births, the Russian foreign ministry prefers, and pays for, diplomats and their wives to fly home. In Moscow, $5,000 will cover the best available care, but many diplomats do not trust Russian maternity hospitals and prefer to stay in host countries. In the U.S., birthing and associated care may cost more than $20,000, a large amount for a family living on a $60,000-a-year income.

In his deposition before a New York magistrate, agent Robertson made it look as though the Russian diplomats were living lives of luxury. He documented their purchases at Swarovski, Apple, Lord and Taylor and Saks Fifth Avenue. The first and second secretaries, however, were not spending like sheikhs or oligarchs: $1,300 cannot buy much at Tiffany. They enjoyed, at best, comfortable middle-class existences. And they saved money for their return to Russia.

"The general atmosphere among some foreign service workers is to save up as much they can for life in Russia," Baunov says. "That means being as thrifty as possible and looking for ways to spend less. Some smarty must have stumbled upon this opportunity and from then on it was passed on by inheritance."

In Russia, scamming the government is a national sport rather than a crime. When Moscow introduced paid parking in a downtown area this year, restaurant doormen started providing a service to clients who wanted to park for free: They covered license plates with stickers so they would be unreadable to parking cameras. The owners of Porsches and Mercedes saved about $1.50 an hour as they dined.

The alleged perpetrators of the health-care fraud will not stand trial because the Russian government will not waive their diplomatic immunity.

Kremlin officials are mad about the case for two reasons. First, they feel the FBI had no right to investigate the diplomats. "All these invented accusations are based on intelligence services' electronic analysis of people's incomes, the movement of funds between their accounts and so on," Deputy Foreign Minister Sergei Ryabkov told the state-owned agency ITAR-TASS news service. "Using such tricks on people protected by diplomatic immunity and carrying official passports contravenes all the norms of international law."

Secondly, it was U.S. Attorney Preet Bharara who spoke to the media about the Medicaid affair. Bharara was banned from entering Russia in April 2013 in retaliation for a U.S. law that forbade entry to the U.S. to a number of Russian officials suspected of corruption. Ryabkov accused prosecutors of taking revenge for "issues that have nothing to do with Russia-U.S. relations."

Despite the two countries' cooperation on global issues like Syria's chemical disarmament, Russia-U.S. relations are in such a sorry state that another diplomatic spat can hardly make them any worse. The 11 diplomats mentioned in Robertson's deposition who are still working in New York will probably have to go home, where their careers will inevitably take a turn for the worse. Moscow will probably find a pretext to expel a comparable number of U.S. diplomats, though it will hardly be able to accuse them of abusing the Russian social-benefit system. When Michael McFaul, the U.S. ambassador to Moscow, broke a finger playing basketball, he traveled to the U.S. for treatment.

Medicaid, however, will still be a system that is almost too easy to abuse. The form the Russian women filled out lists religious, school and medical records as acceptable proof of identity and U.S. citizenship. No wonder the alleged scam went on for years before the FBI got wise to it.

(Leonid Bershidsky, an editor and novelist, is a Bloomberg View contributor. Follow him on Twitter.)