Google is a great tool, but it took me forever to find this:
By forever, I mean it took me almost an hour. That says something about our access to information and my own expectations, but that's another blog post entirely.
The trouble happened because of the nature of my question - which the StackOverflow post does a good job of explaining - I'm trying to call one integration from another. This leads to a semantic overlap of the parts question I'm trying to ask.
I like to envision this as the question collapsing on itself, inside of Google, but I probably don't really understand that as well as I think I do, and I did just watch Tron recently.
Plus many variations of 'call a slash command from web hook on Slack' leads me to Slack's own documentation where they don't answer this question (as of this writing 3/1/2016).
In the end the answer is obvious - you can't call one integration from another. This prevents a lot of attacks or spamming that could probably happen if you had a wide open gateway to push data through Slack.
How did I find it in the end? Brute force querying google until I found a result that didn't look like all the other slash command/web hook posts and documentation that are out there.
Final Google query - 'pass giphy to slack api' which removes the confusion by specifically naming the thing I'm trying to do - 'giphy' - instead of just asking more generally about slash commands.
It was the 4th result.
I have to teach my kids all this some day. Maybe they will just grow up knowing how to do it.