I had this same issue as a Telecom Manager responsible for many Iphones.
We contacted Verizon and they involved Apple support.
It turned out that we had Verizon blocking all PICTURE AND VIDEO Text Messages on the Iphones.
Verizon explained that when you do a GROUP TEXT MESSAGE that include Apply and non-Apply devices, the message has data in it that makes the network see this as a multi-media message.
Verizon removed the BLOCK PICTURE AND VIDEO TEXT MESSAGING; we did a SETTINGS, GENERAL, RESET NETWORK SETTINGS. The device rebooted and the problem is solved.