Well kblaquiere, when you're wrong, you're wrong. (By that, I mean myself.) This is what I did:
1) Delete all music from iPhone
2) Search for the song in my library
3) Delete the song, when prompted to move to Recycle Bin, select "Keep File" (or whatever)
4) Right-click and select "Delete" again. This time I was prompted asking if I wanted to "Hide from iCloud", I'm thinking because it was a purchased song, you can't really delete it from iCloud. I responded "Yes".
5) Added the song back into my Library in iTunes
6) Run Update iTunes Match
7) Played song on iPhone, and what do you know, it played the whole way through, just fine
One interesting thing I noticed is that my song now shows as "Matched" as opposed to "Purchased", which I'm curious if that means anything.
I'm going to try doing this again with some other songs just to test a few things: 1) I streamed the song instead of downloading it and playing it via a play list, I want to see if that makes a difference, 2) I want to see if not hiding it from iCloud makes a difference.
Anyway, thank you for the advice. I still don't understand why or how this works and it makes it even more clear to me that this is a problem that Apple can and should fix. Nothing I'm doing on my end is changing anything on their end. It's not like I'm re-uploading data that is being downloaded to my phone. The song is matched/purchased, and my iPhone downloads from them. This is clearly an issue on their end.