The banks usually have a few brokers they divvy out their REO’s to for sale. There’s no law that says anyone has to use a real estate broker or agent to sell a house unless one wants to utilize the agency laws in the state of CA.
The broker using the MLS eventhough they may want to do it all themselves is a way to make the transaction appear to be “arms length” in nature. The banks may also check the MLS to make sure the broker is actively marketing the houses.
You’d think that being on the MLS about 1 day before going pending would be a red flag for the banks. But they may not look nor care at that point as long as they’re getting the price they’ve been told by the BPO as “good”.