I talked to a Tier 2 rep from Verizon today. She thought it must be a decision by HTC to remove the feature (despite the fact that it's missing from the Lumia as well). So we got an HTC support person on the line and he tried to tell me how to turn group messaging on, and I told him that's the problem, the option is missing. He sounded confused, then put both of us on hold, then came back and said that the software team said that Verizon had flagged group messaging as a "feature block" for them which means they are told to block it from the firmware when submitting it to Verizon.
The Verizon rep seemed surprised by this and couldn't understand why Verizon would have done that. She said she'd try to find out more and call me back in a few days, though she didn't sound very confident of getting an answer.
So, we're still in this weird situation in which Verizon has clearly told both HTC and Nokia to block the feature, though nobody seems to have any clue as to why.
I'll still be returning my phone within the 14 day window unless we get a clear explanation from Verizon as to why this happened and that it'll be remedied soon.