It's been five years or so since I was involved in any QB projects, but at that time all projects were covered under the WTS self-insurance program. However, if any small claims came up the congregation was encouraged to cover these locally so as not to impact the Lord's money.
The society has latched onto the idea of quickbuilds because they save money
Quickbuilds do not save money. In fact they cost more money. When we did a small KH remodel we found that we could do the job for less by finding materials ourselves. Considerably less. Each congregation is assessed a fee to have the Quick Build group involved in the project. This is supposed to cover their phone calls, etc. In reality it becomes a way to collect money, again.
In another state my brother in law reports that an elder was siphoning off some of this money for his personal use. This was hushed up quick. He was never reproved and no money was ever returned to anyone's knowledge.