"Note that it's not always necessary to position things precisely on hot spots or third lines." This comes in a section that starts with "[The Rule of Thirds] is the most fundamental of the rules of composition" in the article on Better Photographic Composition currently on the Luminous Landscape Web site.
Which is it? A fundamental rule, or a rule you can ignore?
This is one of my big complaints about the Rule of Thirds preachers. More often than not they talk about how important this rule is, then you look at their examples and the actual thing that they said should be at a one-third intersection isn't, as in the example in that article.
Composition is about visual balance, and one-third points are just one of many balance choices you can make. They are not the only four balance positions you can choose for something. This notion that it's a "rule" but you can be really loose with it is just pure doublespeak.