https://support.steampowered.com/kb_article.php?ref=7579-RPSX-6098
Yeah, I've seen that before, but I didn't change anything and it suddenly started happening after one of Valve's updates, which made me suspicious.
The only thing it could possibly be on my computer is the firewall, but the firewall simply bothers me for new versions of applications. Even if it was that, I removed the permissions and reset them and it still fails. Putting the dedicated server patch files on the client end doesn't work. Disabling VAC does nothing for it, either. @killermonkey, yes. It happens seemingly randomly up to 5 minutes in.
Thing is, local servers work fine. So all signs point to something being totally borked on Valve's end, at least from my perspective. Thanks for trying to help, though.
EDIT: I take what I said back. It's happening on local servers too.
EDIT2: Nope, I'm wrong again. It seems to only happen on local servers when one side isn't patched properly, but this does not hold with dedicated servers.
EDIT3: ?! I tried connecting to my dedicated server with a patched client earlier and it didn't work, but it does now (at least, it didn't boot me for 7 minutes). I'm confused and/or insane.