A day before announcing that he wanted to withdraw Louisiana from the Common Core State Standards and tests, Gov. Bobby Jindal laid the groundwork for his decision, in part by accusing U.S. Secretary of Education Arne Duncan of coercing states to adopt the standards. He even said that the feds had threatened Oklahoma (which recently ditched the standards) with a loss of federal funding.

“The proponents of Common Core claim it is not a federal takeover, but Secretary Duncan’s comments and actions prove otherwise. He has already threatened Oklahoma with a loss of funding, and we may be next,” Jindal said, according to the New Orleans Times-Picayune.

The problem? Duncan never actually told the Sooner State that it could lose federal dollars if it withdrew from common core. In fact, during a White House briefing, he said precisely the opposite, in response to a reporter’s question about Oklahoma’s funding future.

“We are partnering with folks who have high standards. If people want to dummy down standards, that’s a very different thing. We partner with states whether they’re in common core or have their own high standards. But where we will challenge status quo is when states dummy down standards,” Duncan said.

It’s true that, in signing the bill that repealed the standards, Oklahoma Gov. Mary Fallin, a Republican, said it was “a possibility” that the state could be jeopardizing federal funds.

But, now that the law has been changed for a couple weeks, Oklahoma isn’t particularly worried about the loss of funding—and Oklahomans say the Obama administration never actually “threatened” the state, as Jindal contends.

“Oklahoma has not been threatened with the loss of federal funds for the repeal of common core. We don’t see that as a possibility, really,” said Phil Bacharach, the executive director of communications for the Oklahoma State Department of Education.

Does that mean that Jindal’s broader point, that the feds “coerced” states into adopting Common Core is also bogus? That depends on who you ask. The Obama administration gave states that adopted uniform, rigorous standards an edge in the Race to the Top competition (in practice, only common core fulfilled that requirement).

And the education secretary called for states seeking waivers from the many mandates of the No Child Left Behind Act to embrace standards that would get students ready for post-secondary education and the workforce. Common core met that requirement, but states could also develop their own standards, with the blessing of their post-secondary institutions, which is the point Duncan was attempting to make the press briefing. Virginia and Texas, for instance, went this route.

So where did Jindal and Fallin get the idea that money could be on the line if their states ditched Common Core? Both states currently have waivers from the NCLB law, and it’s possible that the states could risk that flexibility if they don’t come up with other standards that meet with the approval of their post-secondary institutions.

But there are two things to keep in mind here, says Anne Hyslop, a policy analyst at the New America Foundation. First off, the department has been reticent to pull waivers from states because of issues with standards and tests—so far, only Washington state has lost its waiver, and that was due to teacher evaluation issues. And other states on “high-risk status” are there because of teacher evaluation, too, not standards implementation.

Secondly, even if a state loses its waiver, it doesn’t actually lose federal funding. It just means that districts in the state would lose flexibility over Title I dollars; they would have to spend that money on school choice and tutoring instead of their own remedies. That’s not great, and states might “feel like [they’ve] lost something, but what they’ve lost is flexibility,” Hyslop said.

Louisiana is a bit of a special case, Hyslop added, because it won a small, late-round $17.4 million Race to the Top grant, which is dedicated, in part, to beefing up standards. So there’s a chance Jindal’s move, could ultimately put that funding at risk. (More on that in this great Hyslop piece.)

But that’s not something any state that has ditched common core, including Oklahoma, has to worry about.