The undercover videos purporting to show officials of Planned Parenthood bargaining over the sale of fetal tissue have made the promise to defund the organization one of the most popular refrains on the Republican presidential campaign trail.

It’s actually a much easier promise to make than to fulfill. But that’s not slowing down the candidates.

“There is no reason in the world to have Planned Parenthood other than abortion,” said Sen. Rand Paul, R-Ky. “We should stop all funding for Planned Parenthood.”

Carly Fiorina, former CEO of Hewlett-Packard, echoed many of her fellow candidates by vowing that “we should shut down the government” rather than allow further funding of the organization. Many Republicans – though far from all – have been advocating a fight over Planned Parenthood funding this fall when it comes time to keep the federal government operating.

Candidates that are or were governors have gone even further – saying they have already eliminated funding for the organization in their states.

“I defunded Planned Parenthood more than four years ago, long before any of these videos came out,” said Gov. Scott Walker, R-Wis., in the recent Fox News debate.

“As governor of Florida I defunded Planned Parenthood,” said Jeb Bush, who served from 1999 to 2007, at the same debate. “I created a culture of life in our state.”

But did they really? That depends on how you define the word “defund.”

Both Walker and Bush (along with Gov. Chris Christie in New Jersey and former Gov. Rick Perry in Texas) did reduce state funding for the organization, mostly by cutting off long-standing grants earmarked for family planning programs. (With few exceptions, funds for family planning may not be used for abortion.)

But while the cuts forced the closure of some Planned Parenthood clinics, all four states still have Planned Parenthood clinics operating there, in some cases still collecting state as well as federal funds.

That’s largely due to a requirement in the Medicaid program, from which Planned Parenthood gets most of its government funding. Medicaid funding is shared between the federal government and the states, although the federal government pays 90 percent of the cost of family planning services.

“There’s a requirement in the [Medicaid] statute for free choice of providers,” said Cindy Mann, who recently stepped down as head of the federal Medicaid program and is now with the law firm Manatt, Phelps & Phillips. “The only way you can limit the provider is to establish that they’re not, in fact, qualified as a Medicaid provider.”

Federal courts have agreed. In 2011, the last time Planned Parenthood was in the headlines, Indiana passed a law barring Medicaid funding to any entity that also performed abortions, even if those abortions were performed with non-public funds. A federal appeals court ultimately blocked that part of the law because it interfered with the Medicaid law’s “freedom of choice” requirements.

“Although Indiana has broad authority to exclude unqualified providers from its Medicaid program, the state does not have plenary authority to exclude a class of providers for any reason – more particularly for a reason unrelated to provider qualifications,” wrote Appeals Court Judge Diane Sykes in the majority opinion. Sykes was appointed by President George W. Bush.

Congress, of course, could defund Planned Parenthood by changing that requirement in Medicaid law.

But Medicaid experts say recent announcements by the GOP governors of Louisiana and Alabama that they are also attempting to evict Planned Parenthood from the Medicaid program in their states are unlikely to become reality.

Louisiana Gov. Bobby Jindal, who is running for president, said in the debate for the second tier of candidates last week that “we just, earlier this week, kicked them out of Medicaid in Louisiana.” None of the Planned Parenthood clinics in the state perform abortions.

In Alabama, Gov. Robert Bentley notified Planned Parenthood last week that he would be ending their contract with the state to serve Medicaid patients. “I respect human life and do not want Alabama to be associated with an organization that does not,” he said.

Neither of those actions is likely to succeed, said Sara Rosenbaum, a law professor and Medicaid expert at George Washington University.

“This is a right for beneficiaries going back to the original statute,” she said, referring to the ability for patients to choose their health care provider. She added, however, that governors wishing to use the exercise for political gain “have nothing to lose,” because it is now up to the providers to sue.

Planned Parenthood has not said yet whether it will challenge the Alabama or Louisiana actions in court.

One way GOP governors have managed to cut Planned Parenthood funding is by dropping out of an optional Medicaid program that provides federal funding to pay for family planning services for women who don’t otherwise qualify for Medicaid, but who still have low incomes (usually under twice the federal poverty level, or about $23,500).

That’s how Texas partly defunded Planned Parenthood in 2011. When Medicaid officials said the state’s new law barring funding of organizations that also do abortions violated the federal free-choice-of-provider requirement, Texas was actually expelled from the expanded family planning program losing its federal funding. The state instead created its own program with (substantially less) state-only money. Planned Parenthood had been providing just under half of the services for the entire program, so excluding the organization meant women in Texas had trouble getting family planning services.

According to the Texas Policy Evaluation Project, which is studying the impact of the changes, by 2013 the reductions caused 82 clinics (not all Planned Parenthood) to close or stop providing family planning services and prompted others to limit the types of services they provide, as well as ask women to pay more of the cost themselves.