Which rule states that parses can't be posted in chat?

[Astrus]

Using any third party software is against the ToS. If you post a parse result in chat then the implication is that you are using a parser, and because that information can only be gotten from third party software you're basically saying "hey look at me, I'm breaking the rules!".

There's no law that prevents you from shouting "I robbed the old lady down the street" but if you say it around the wrong person or say it enough times, you are going to draw attention to yourself and get your activity investigated. The same applies to talking about parse results in chat.

You're not going to get away with posting parse results by saying "there's no rule against posting them" to a GM.

Which is precisely what my post you quoted goes on to say, glad we're on the same page.