The REST example, at:
https://developer.atlassian.com/confdev/confluence-rest-api/confluence-rest-api-examples#ConfluenceRESTAPIExamples-Addacommenttoapage%28python%29
Well, where do I start? First, to even read it, let alone attempt to run it, one must convert and remove HTML entities.
Now that you can read and run this script, you'll want to replace localhost:80 with the URL of a hosted Atlassian instance, and, at least in our case, also replace /confluence/ with /wiki/, substituting known creds in your instance for admin/admin in the example.
Now, fancy things start to happen! The first part of the script, which performs a search to get the id and other info about the page, works correctly. If I print the JSON, it describes the page I'm trying to post to.
The second part, which conjures JSON to post the comment itself, results in a response which, if I run the script with python -i and print request.text, is literally a random ass page in the wiki, seemingly created as a test by our CTO months ago. It might be the first page in the wiki, I can't really confirm that.
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I'm sure, if you've read this far, you're all, "Dude! There's documentation for the REST API! Just read!"
Is there? Really? Documentation for the REST API? Let's take a look! 
Ohai, on https://developer.atlassian.com/confdev/confluence-rest-api , there's a link to the above page!
Let's skip that, since we've been there. Here's the documentation for the REST API that the Python example above is POST-ing to:
https://docs.atlassian.com/atlassian-confluence/REST/latest/#d3e865
So, the documentation for GET specifies the possible valid values for "type" as "page" and "blogentry". I'm willing to accept that POST may have a special case for "type":"comment", but the documentation for POST literally just confirms that you can POST.
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Now, you might be like, "Again, dude, there's an API browser! Why not try that?" Well, first, I'm going to say it should be safe to assume that the API browser would not contain more information than the documentation, but I'll tell you how hard I tried to solve this ridiculously stupid problem - I tried to use the API Browser.
The documentation provides unix commands for running on my Confluence server to run, tells me to install an Plugin SDK, etc.. I don't have a Confluence server, I don't want to write plugins, I just want to use this one API in hosted Confluence. 
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So, Confluence community - please assist! I'd love to even contribute a fix for the documentation to Atlassian.
I just.. just... really want to post a comment from Hubot, but I can translate the Python to Coffee Script. As a matter of fact, I already have. I didn't even try the python example until I wanted a more familiar language to figure out why my CoffeeScript wasn't working.
I'm pretty sure it's not my CoffeeScript, having spent many hours with this python code. 