Reading the whole story both the pilots union and United are trying to pin the entire blame on the airport police, while United is setting the stage for limiting their exposure and pointing out the flight and plane are owned by Republic, not United.
First - the pilots are going to take a hit, the captain was in charge of the plane and he was responsible for letting people on to illegally remove a boarded passenger.
Instead of scrambling to limit liability, both the pilots union and United should be scrambling to fix the mess United is responsible for with their bureaucracay.
1. Get their procedures in line with their Contract with passengers.
a. Denied boarding means denied boarding - get a legitimate process for determining who can board and who can get “bumped” and implement it before boarding - recognizing once they are on the plane they have no right to take anyone off (unless the passenger violated one of the enumerated, contractual provisions in their contract Rule 21).
b. Give the gate agents more authority for increasing amounts for volunteers to be bumped - and streamline the process to go beyond a limit - create a hotline to the company to deal with situations such as this where they will need to exceed their authorized amounts.
2. Recognize their reputation for treating passengers poorly is more than justified, and that they are taking immediate steps to fix it.
a. Go the extra mile - proactively state that while they are in the process of a thorough review of procedures there will be no involuntary bumps for flight crew / employee transportation priorities - only voluntary bumps - for at least the next 60 days.
b. Priorities will go to ticketed passengers with assigned seats in making any involuntary bump for other reasons.
There are lots of things they can do - and they should not let another day go by without some concrete action beyond no longer calling on the police to remove passengers. Frankly, United’s suggestion that they won’t do that anymore is beyond laughable - they never had a right to call the police in the first place for removing a passenger not in violation of rule 21.
Which isn't going to convince anybody. You book on United's website. Your ticket says United. Your bill is from United. You get United frequent flyer miles. No one will care who the sub-contractor is, it's all on United.