AOL CEO Tim Armstrong got in some hot water yesterday when he cited the medical expenses of two employees’ difficult births to explain why the company will make its retirement plans less generous.

The ire was immediate: How dare Armstrong (perhaps America’s most gaffe-prone CEO) single out these two women’s health care costs as a reason for cutting back on every employee’s 401(k)—especially when he’s personally on track to make $12 million this year?

The CEO brought up the births, which apparently cost $1 million each in medical expenses, as an example of how health care costs are eating into other benefits—specifically, that the added costs that come with the new health care law, some $7.1 million, were the driving force behind the change to retirement plans. Instead of matching employees’ retirement savings immediately, AOL will do so in a lump sum at the end of the year, limiting workers’ investment return.

Armstrong’s stance fits in with that of other American CEOs who have blamed Obamacare’s requirements that they offer their workers high-quality health care plans as a reason for letting workers go or raising prices. Many restaurant chains who rely on part-time workers, including Papa John’s, Applebee’s, and Darden Restaurants, parent of Olive Garden and Red Lobster, have cited the law as a reason for unpopular cost-cutting measures. They’ve gotten some flak for saying so, but by and large people accept the logic.

Yet what they’re saying is essentially the same as what Armstrong said: While not every medical problem is as critical or expensive as a sick infant (and singling out specific employees is extra gauche) companies are facing a trade-off between their employees’ health and their profits. Since the law mandates the former and their jobs the latter, they’re going to find other ways to cut—probably, though, not in the executive compensation account. All this might be enough to make CEOs wish they weren’t in the business of providing health care at all, but political pressure to build on the existing system—provided in part by the business community—led lawmakers to graft new expansions of coverage on top of employer-provided health care coverage.

As the health care law continues to come into force, the “Obamacare made me do it” excuse may prove convenient among corporate executives addressing all manner of tricky challenges—price hikes, benefit cuts, lay-offs. When they use it, they’d do well to remember Tim Armstrong and those sick babies.