The attack they're describing is a dictionary attack, and it's very common. A simple script, 20 minutes or so and if the website in question doesn't have specific measures in place to counteract it, an account can be cracked.
I do generally follow secure password policy. My only conceit is that I do reuse passwords to some extent. I have a list of them memorized and will select one more or less at random for a new account. One of the benefits of this system is that if I should forget what password goes with which account or website, I only have to guess a limited number of times before I hit on the right one. The monumental downside is that if someone were to somehow obtain a list of all my passwords they'd have access to basically everything.
The principles of a strong password have been understood for a long time. No words, mix of numbers and letters, mixed case, at least 8 characters. If more people followed these guidelines there'd be less cybercrime. It's as simple as that.
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I wake up in the morning more tired than before I slept
I get through cryin' and I'm sadder than before I wept
I get through thinkin' now, and the thoughts have left my head
I get through speakin' and I can't remember, not a word that I said
- Ben Harper, Show Me A Little Shame
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