Please expand upon this statement.
Sure.
In its default configuration, the 'login' keychain is always unlocked. This is convenient for applications because it means that they can access it without prompting you.
According to SubRosaSoft, however, that very setting can be exploited to recover everything in the keychain, even from a Mac that's been put to sleep. Now I don't have ready access to MacLockPick, so I can't elaborate on exactly why it's able to do what it does, but my bet is that if a commercial software developer has figured out how to exploit that setting that the blackhats also have a pretty good idea.
It gets worse though. When last I heard (2008), loginwindow.app didn't purge the login password from memory. Since by default the login password is also used as the keychain password, any app that can get access to the memory address where it's stored will have access to the keychain. Getting access to that memory might be tricky, but it's not impossible (anything that's got root permissions or is doing DMA can do it).
So yeah, maybe "one of the worst things you can do from a security standpoint" was a bit harsh, but it's still, at least in my opinion, a pretty bad idea. IMO a false sense of security is far worse than a lack of security.
The Keychain solves this problem by allowing you to use strong passwords without having to remember them.
I disagree. The Keychain simply changes the attack surface by giving your security a single point of failure. An attacker seeking to gain control of, say, your e-mail accounts no longer has to guess each password individually -- he just has to guess a single password, after which he has access to your e-mail, stored web site passwords, secure notes, and more. I'd argue that's a more dangerous proposition.