As the Times points out there are unintended consequences. Ecology is a science of complex systems. But they didn't go quite far enough in analysis - a burgeoning mouse population is met by an increase in natural predators - coyotes, wolves, bobcats, hawks, etc. If they're allowed. Some of these find the livestock that was the original motivation for eradicating knapweed right tasty. Welcome to the real wild world. We can affect it but I don't think we can really manage it, not this way, at least.
Thanks for the follow-up!