This issue seems to have to do with carrier provisioning for the phone and the phone's network settings. Redoing them appeared to fix it.
The Fix:
1) Ask carrier to re-provision the phone. My carrier was TMobile. This may delete voicemails, so save them if needed.
2) On the iPhone, Reset Network Settings.
A little more detail about my case.
- I can send any one or group of iMessage recipients text or images, no problem.
- I cannot send images+text to text recipients, BUT images are heavily downsampled.
- I can send text-only messages to text recipients.
- I cannot send text-only messages to group text threads.
- I can send image+text to individuals if I turn off MMS.
- I can send text-only messages to group text threads if I turn off MMS, BUT they appear as direct messages to each recipient of the group.
For the last point, you can imagine comms to be pretty awkward. "James, I'm down to go." sent to a person named "Sarah".
What seems to be happening is SMS works, but MMS does not work.
Anyways, this **** irked me for months. Finally got it fixed. Hope you can have same lucks me.