I've been having this issue for years and today I finally found a solution, so I feel it's my civic duty to share what I did with others. So I did two things that resulted in being able to receive iPhone group texts (and receive them in the single string), so it's impossible to say which step was the difference maker but at this point I'm just happy it works.
#1 I logged into my Apple account (had to dig up my ID and password) and deleted my phone number from my account information. I had read on this thread that it can make a difference.
#2 I downloaded the Go SMS Pro App. I altered the settings of this app slightly by go to Settings>Send and Receive Settings> (to the bottom) check MMS Group Chat
It appears that the phone is still receiving the blank texts but then immediately converts them into a single group message string.
It's not perfect but it sure beats getting endlessly frustrating blank iPhone group messages. I hope it works for you too!