Frankly, this is the weirdest complaint I've ever seen about checked exceptions. If you're trying to build a system with crappy programmers, you're kind of screwed anyway, but checked exceptions actually help you out quite a bit, because you don't have a problem with stray exceptions taking down entire subsystems. You might miss a lot of meaningful errors and get corrupted data, but at least the system keeps running, and that's the most you can hope for if your programmers are as crappy and lazy as the article describes.
And contrary to the article, few programmers are really that lazy and irresponsible. In my experience, far more code is written by responsible programmers who are inexperienced, rushed, or lacking a complete understanding of the system. Checked exceptions catch a lot of normal programming errors and result in more error cases being handled correctly. Like any other restriction imposed by a programming language, they don't ensure perfect code, sometimes they result in busy work, and crappy programmers will find crappy ways to work around them, but IMHO they are helpful for most programmers.