The first link doesn't seem to mention this particular topic at all, while the other two are both internally inconsistent and unclear, let alone consistent with eachother and basic logic.
You can drop your mic all you want, but it doesn't automatically make you right. You also seem to be a child worker with a superiority complex ...
You must not be very good at reading English. The first link is directly on point, e.g.: Your claim to be a "first language English-speaker" is beginning to lose credibility. Actually, even that phrase, "first language English-speaker" casts doubt on your claim. I've never heard a native English speaker use it, and I've never seen "English-speaker" with a hyphen like that (as opposed to "English-speaking <insert_noun_here>") because that's incorrect use of a hyphen. Trolling: it's not just for bass any more, is it?
Yeah, well, in my experience hypercorrection sometimes gets the best of us all, even inclusing pesky dimwits like myself.
In hindsight I should have realised. It's the same with legal jargon - an agreement is lower case because it could be referring to any old agreement but the Agreement is capitalised because it referrs to a specific Agreement.
It refers to an agreement called Agreement (Something Something), though, right, not simply a specific agreement? We don't write "The Car is mine." or "I'll bring the Fishing Rods." after all. A referent is not the same thing as a title.
I am referring to, for example, a document talking about an Agreement to Lease. So it could be a specific Agreement to Lease i.e. Joe Brown will lease Shop 1 from Emily Smith or a generic Agreement to Lease, either way it would be capitalized because it's referring to the name of a particular agreement rather than any agreement. So the text could read something like `Mr Brown will sign the Agreement tomorrow but we reserve the right to have our lawyers read over the Agreement beforehand. However, please be aware that not all agreements will meet our requirements.` The basic rule of thumb (when I was doing legal work) was that if it had the word 'the' in front of the document it would be capitalized, if it didn't then no caps. I know it's not the same as writing fiction but I think it has the same basic rule. It makes sense to me at least.
I'm an attorney, and while what you describe does occur in legal writing, there's an effort to phase it out and use plain language instead. No more "Party of the First Part" nonsense. That said, just as you might name a dog Dog, the use of things like "this agreement (hereinafter, the Agreement) to lease the above-described rental property (hereinafter, the Property)" has some advantages if used in moderation.
That's still a title, though. In a legal setting it has been decided that something is to be called an Agreement, as a made-up name akin to how businesses and products are named. When you call someone "friend", on the other hand, you're not doing so because a group of people got together and decided what a friend is and who's friends with whom.
