They are just talking about long-term disability!? I have it as well, for mostly the same reasons. I worry that if something were to happen to my hands, eyes, or brain that I wouldn't be able to provide for myself or my family.
I don't think having disability insurance is "that much worry".
That sounds like a person who is on a lookout for something to be worried about, pretty much the definition of anxiety.
On the other hand, i think disability insurance is not even a little bit crazy; Of course, know that if you use it, you'll probably use it because you got screwed up in an auto accident (few people carry enough insurance to cover lost work for a software engineer for very long) but I think auto accidents are common enough to want to hedge against it.