Stock LG messaging app, stock dialer. Rooted device and that's about it. I noticed I actually do not need mobile data on to send and receive picture messages normally (not in a call) so I typically leave it off when I don't need it for data.
My setup when I tried was WiFi on and connected to my home network, mobile data off, and phone call present. Would not allow me to send the picture. I'll try it with data on later and see if it works.
Didn't think it was a law, Which is good. May be that the data was off. And yes Verizon phones do not send pictures through WiFi they do need mobile data for Verizon services (text,MMS).