First, this is why I never allowed anyone with Progressive to sub-contract thru me (was a carrier not a broker but did interline some work).
Second, Progressive really can’t deny the claim when a third party (your customer) is involved. If they carry the MCS-90, which they should if the motor carrier has proper operating authority, they are bound by Federal law to be responsible for everything that happens under the direction of that motor carrier.
Example, I have had unauthorized use of my US DOT number before by a disgruntled ex leased-on owner op, he kept displaying my number and had a crash. I was, or my insurance carrier was, responsible to pay that claim even though the ex driver was fraudulent in their activities. This is why it is so hard to take insurance coverage off a commercial truck if you are just parking it, because listed or not the insurance carrier that issues your MCS-90 is liable.
The same premise applies to drivers. I would start with a higher supervisor at Progressive, if they won’t work with you inform them you are calling the state insurance commissioner office to lodge a complaint.
You may also have to start a lawsuit against the carrier. This will force Progressive to get involved since they have a duty to defend their policy holder, plus if the motor carrier happens to have any excess lines (blanket, general commercial liability, excess cargo, etc) a lawsuit will open up access to those policies.
Oftentimes once faced with a lawsuit the insurance company will pay nuisance claims just so they go away.