On March 13th, House Speaker John Boehner held a press conference. By that point, Obamacare enrollment was beginning to accelerate. But Boehner thought it was an illusion. He wanted to change the narrative. And so he made a startling claim: Obamacare, he said, had led to fewer people having health insurance.

Reporter: Mr. Speaker, you said a minute ago there are fewer people today with health insurance than when the law was passed. I want to make sure I understand. You're saying that Obamacare has resulted in a net loss of insurance? Boehner: I believe that to be the case. When you look at the 6 million Americans who have lost their policies and some — they claim 4.2 million people who have signed up — I don't know how many have actually paid for it — that would indicate to me a net loss of people with health insurance. And I actually do believe that to be the case.

Boehner was going off of claims and guesstimates. He admits as much in his answer: this is what he believes, not what he knows. But a new report from the Rand Corporation gives us a fuller picture than ever before. And so now we know: John Boehner was wrong.

1) 9.3 million more people have health insurance

Washington has been tracking enrollment in Obamacare's exchanges and, less precisely, in Medicaid. The Rand study uses a nationally representative sample to track vastly more data: they know roughly how many people were buying insurance from their employers, from insurers, and much more. They also know how many people were losing insurance, either through cancellations, or because employers were dropping them, or because they just stopped paying premiums.

Add all the gains and all the losses together and you get Rand's bottom line: 14.5 million people gained coverage, 5.2 million people lost coverage, and so the net change since 2013 was 9.3 million people getting health insurance.

2) An unexpected Obamacare success: more employer coverage

One major finding in the Rand study: on net, more than 8 million people gained insurance through their employers. And most of those people were previously uninsured. That's a huge deal.

Rand speculates that some of the increase might be people buying insurance so they don't have the pay the individual mandate, and some of the people might be getting new jobs that offer insurance because the economy is improving. Either way, predictions that Obamacare would lead to employers throwing people off insurance are, at this point, proving completely wrong.

3) The uninsured population has fallen from 20.5 percent to 15.8 percent

That's a sharper drop than Gallup has found, though both surveys show that the number of uninsured is falling fast.

4) People are always losing health insurance

Something the Rand study does a nice job of showing is churn. Health researchers know that people are always gaining and losing health insurance. Folks get fired, or they get hired. They become poor enough to get Medicaid, or rich enough that they no longer qualify. The question is whether the gains outweigh the losses.

This churn has been a particular problem for Obamacare because the law is being blamed for the kinds of insurance losses that happen all the time anyway. In a way, the law has been a huge boon to employers who wanted to cut benefits to save money, or insurers who wanted to close down an insurance pool that was no longer profitable. Now they can just blame Obamacare.

The Rand study is really the first that lets us see the full extent of that churn. For instance, it tells us that about two million people who had insurance-based coverage in 2013 lost it by March of 2014. But more than seven million people who were uninsured in 2013 got employer-based insurance by March of 2014.

If you want to dig deep into this issue, there's an interesting Twitter conversation on it between Ben Domenech and Adrianna McIntyre.

5) Many more people have gained insurance since the study

Rand is very upfront about the fact that much of the data for their survey was collected in early March — before Obamacare's massive, end-of-month surge.

Moreover, enrollment in Medicaid is still open, and Obamacare is also still signing people up into the exchanges through various deadlines and loopholes. So it's certain that hundreds of thousands — and perhaps millions — more people have gotten insurance since the Rand survey ended. So think of this as a low-end estimate.

6) 80 percent of people are unaffected by Obamacare.

Obamacare was built to leave most people alone. And the Rand survey shows that it's succeeding in that. "The ACA has not led to changes in the health insurance coverage of most people," Rand says. "Among adults, fully 80 percent still had the same form of coverage in March 2014 as in September 2013."