This is true, but it's true for almost every observational study, and IMO too easy a dismission. You can use this reasoning to dismiss, or more likely, to cherry-pick probably 95% of all scientific results from economic/medical/social/nutricion/climate science. Just imagine the actual mechanics of setting up a proper Randomized Controlled Trial of seat belt safety!
Back to the actual study, the reasoning appearch to hinge on the variation of outcomes between 1) having a 2nd and 3rd child 2) between car and non-car owning families 3) accross different states in the US with different introduction dates between car seat laws. Of course, their might still be lurking confounders, but the presumption that this is really caused by car seat laws sounds quite convincing to me[1]. I'd say the onus on sceptics in this case is to actually propose some possible confounders that might explain variation in all of 1), 2) and 3).
[1] Disclaimer: I haven't gone through the details of the paper to see if the idea is actually well executed. This paper is likely headed for a serious economic journal, where it typically goes through at least days of labor to scrutinise the execution/details/methodology in peer review. I'm not invested enough to volunteer for that.