I don't know about other countries, but in India, the branch had helped us out with rebuilding our homes during the 2004 Tsunami and other floods thereafter. So out of my experience:
whether the org really does take insurance money from disaster victims after the RBC / LDC repairs their homes?
Not here in India
And what of non-JWs that might get assistance from them?
Assistance? The locals ambushed and looted most of the relief supplies sent by the branch and other JW's. At checkpoints, police used to frisk these trucks and kept 1 out of 3 items for themselves. You can see videos of locals pulling jewelry out from the dead bodies.
I live in a city of 1.8 million people with only 150 JW's. So during a flood, by the time WT supplies reaches these JW's, thousands in between would have chewed and helped themselves from these supplies.