Yesterday, the Administration released data from the 2011 National Health Interview Survey that shows, among other things, that the number of uninsured young adults declined over the last year. In a short press release, the Department of Health and Human Services (HHS) touted this as evidence that Obamacare is working, specifically attributing increased coverage of young adults age 19–25 to the Obamacare provision allowing those individuals to stay on their parents’ health plans.

Undoubtedly, it’s true that some of those individuals did get coverage due to that provision, but HHS claiming credit for Obamacare for all of the increase appears to be an example of the classic statistical fallacy of confusing correlation with causation. Even more importantly, over the long term, the net effect of Obamacare’s many provisions will be to increase the already unaffordable cost of health care, which is one of the main reasons young adults and other uninsured forego coverage.

The Administration claims that the percentage of uninsured adults age 19–25 declined from 36 percent before passage of Obamacare to 27 percent in the second quarter of 2011, a decrease of 2.5 million individuals. In fact, the report they reference shows that uninsurance in that age group actually dropped from 33.9 percent in 2010 to 28.8 percent in the first six months of 2011, a decrease of 1.3 million.

Moreover, the data also show the same coverage trends for older, working adults. Between 2009 and 2010, the number of uninsured grew, but then, between 2010 and 2011, it fell. It thus seems likely that at least some portion of this variation in coverage was due to the U.S. entering, and now beginning to exit, a recession. As individuals lose jobs in a recession, many lose their health coverage, and as an economic recovery occurs, the opposite occurs.

Regardless of whether or to what extent the White House is correct, allowing young adults to stay on their parents’ plan does little more than cover up a fundamental problem left unresolved under Obamacare. It’s clear that the reason for uninsurance for many Americans, not just young adults, is not lack of access. Instead, it’s the increasingly unaffordable cost of coverage. Obamacare will not only fail to slow runaway health care costs but will instead cause premiums to skyrocket as the rest of its provisions go into effect between now and 2014.

Already, parts of the law, including the requirement that young adults up to age 26 can stay on their parent’s plan, are increasing premiums. Projections from Deloitte, a benefits consulting firm, show increases of 1–2 percent from this provision alone.

And that’s just the beginning. As the rest of the law is implemented, small jumps in cost will quickly add up to a sizable chunk of change. Heritage analysts have identified at least 12 provisions of Obamacare that will increase premiums. Beginning in 2014, insurance plans will be required to offer a government-approved minimum level of coverage. As Heritage expert Ed Haislmaier explains, “The more benefits providers are able to have deemed ‘essential,’ the more insurers, employers, and patients will have to pay for these services. The result will be higher premiums for tens of millions of Americans.”

Other insurance requirements—such as no cost-sharing for preventive services, limits on other cost-sharing and deductibles, elimination of annual and lifetime limits, and guarantee issue—will further ratchet up costs. And then there’s the impact of new taxes on insurers, medical device manufacturers, and pharmaceutical companies, the cost of which will be passed on to consumers.

Even if young adults do stay on their parents’ plans, they don’t face a pretty scene once they become too old to do so. Several independent studies have shown that the biggest increases in premiums will fall on the young and healthy purchasing insurance in the individual market. MIT economist Jonathan Gruber and Gorman Actuarial show that, in the state of Wisconsin, those age 19–29 who purchase insurance in the individual market will see an average increase in their overall premium of 34 percent.

So Obamacare will not eliminate one of the main barriers that young adults and other Americans face to obtaining coverage. Instead, it will make matters even worse.