The big Obamacare news on Tuesday involved a pretty big number: 9.3 million. According to the Rand Corporation, that’s how many more Americans have health insurance thanks to the Affordable Care Act. Maybe.

Like similar studies from Gallup and the Urban Institute, Rand’s has a high margin of error and depends heavily on people responding to questions accurately. That doesn't always happen. In addition, the Rand survey suggests that the number of people with employer-sponsored insurance grew by 8 million. That would be a lot higher than what the experts had predicted. And that makes me wonder whether the estimate is right.

None of this is a knock on Rand (which, in its writeup, was quite candid about the study's limitations). It’s just a reminder that you shouldn’t take the specific figure too seriously. It tells you the number of Americans without insurance is declining. It doesn't reliably tell you by how much.

But it was another finding in the study that caught my attention:

Less than one million [people] who previously had individual market insurance transitioned to being uninsured. While we cannot tell if these people lost their insurance due to cancellation or because they simply felt the cost was too high, the overall number represents less than one percent of people between the ages of 18 and 64.

Republicans and their supporters frequently say that 5 million people “lost” health insurance, because the old policies didn’t comply with Obamacare’s standards and/or insurers cancelled them pre-emptively. Sometimes Republicans and their supporters imply that these people actually ended up uninsured. But if Rand is right—and, again, there's no way to be sure right now—then it would appear most people who lost their old plans were able to get new ones instead. That's consistent with anecdotal reports from insurers.

To be clear, that doesn't mean people who lost their old insurance policies are happy about the change—or that they don't have a legitimate beef with the president, who famously promised that Americans could "keep their plans." Some of these people are now paying more for their coverage. Some have fewer choices for doctors and hospitals.

But plenty of people who lost coverage were able to replace it with plans that were cheaper, more comprehensive, or both. In short, not all the 4.8 million people who lost their old coverage are worse off. It's not even clear that a majority of them are. That's one more reason the case against Obamacare may be even weaker than you've heard.