"SMS message delivery not guaranteed" is a pretty remarkable cop out!
I was surprised how hard it was to find any other mention of it. Mostly recent Samsung devices are the source of the problem, and one thread noted many other receiving phones besides Windows Phones not getting it, as I see on my mom's flip phone.
IPhones are the only others not seeming affected, but apparently this feature was made to emulate the messenger service on iPhone, so...
One thread suggested special provisioning of the source device may have helped but there was no follow up.
My 950 has Straight Talk service through ATT. I tried some newer APN settings, but there was no effect.
I want to say I didn't have this problem on my 735 with WP8.1. However now I'd have to go check. It did start having strange MMS problems in groups. But I'm not sure failed delivery was one, except one Samsung device that consistently "sent" blank group messages to it.
If there's anyway to fix this on the receiving end, it'd be fantastic! Since as witnessed with my cousin, she didn't want to keep it off once she noticed the side effects.