I tried those options and sent a picture message to my cousin.  It shows only "Sent" on my side  and she did not receive it.  

I sent the exact same pic to my sister who is also on Verizon on a completely different account from myself and my cousin.   When I sent the same pic to her, it went to "Delivered" on my side and she got the pic.

My cousin receives pics from other Verizon customers.  It is only me that we have noticed she does not get them.