Questions about renting to a displaced family

Recently, we had a third party reach out to us looking to help place a displaced family due to a house fire at our rental property. The third party operates out of a different state (odd thing is we had 2 separate companies who seemingly do the same thing reach out, assumedely for the same family since each was within a couple days, one from FL and the other from CA, and our property is in the midwest). We showed the house to the family and they're interested in staying, however, I just found out that the third party is who will be on the lease, which is what I'm confused about. Apparently the third party works with insurance companies to place displaced family's, and apparently they sign the lease, and I guess her a cut from the insurance company for helping to place the family (I'm not sure what the arrangement is exactly though). Am I wrong in being worried to not have the people staying at the house on the lease? The whole situation is something we've never dealt with as we typically rent to traveling nurse, but it seems odd, and I just want to avoid any issues. Does anyone have any experience with this, or any advice on how to structure the lease?