Stress-testing, shared-nothing and dollar-scalable are platonic ideals, and they're not always achievable. If Dropbox had three infrastructure engineers, they probably weren't able to build proper capacity planning models, and probably couldn't afford to build a full production work-alike for stress testing anyway. (And at some scales, that's literally impossible. Our vendors couldn't physically manufacture enough servers to build a full test environment, cost aside.) I'm sure they did some simulated tests as well, but those won't tell you the whole story.
You're focused on IOPS, but you have no idea if that's what Dropbox's bottlenecks were. (Not to mention: What does IOPS mean on an EBS and S3 infrastructure?) Complex systems fall over in complex ways. You can predict the next bottleneck, but not the one after that; by the time you get there, your fix for the first bottleneck will have changed the dynamics.
It sounds like they did do stress testing, using real-world loads, on a system that was 100% similar to their production system. They ran continuous just-in-time stress tests in the Big Lab.