Damage question from renter's perspective - sideswiped by NYC bus

Rented a vehicle and was side-swiped by a bus in NYC area last weekend (4/26). Submitted damage through the app and the host chose to resolve directly with me. I helped the owner submit a damage claim form to MTA (owner of the bus, employer of the bus driver, etc) for damage related to the host's vehicle, which the owner submitted on 4/29. Today I received this from the owner:

Unfortunately I have been unable to contact anyone from the bus driver’s insurance company I have sent the form but they haven’t reached out at all. The best option would be to unfortunately file with your personal insurance to get the damage fixed then your insurance will get reimbursed from the bus driver insurance through subrogation at the end of the claim. This has to be done soon as I have only 20 days to default back to Turo insurance. Your insurance has to approve the damages within that time so have to get this started asap. If we end up going with Turo insurance it could go one of two ways, either you would pay me your out of pocket maximum $3000 after I request it through Turo and I pay the difference to get the vehicle fixed, or if you deny the payment it will default to the insurance so I will pay my $2500 deductible and insurance covers the rest but you still pay your maximum $3000. So option 1 filing with your insurance is the best, worst case option 2 you pay the maximum then can try to get reimbursed potentially. I really don’t want it to go to option 3 Turo insurance as it is the worst for both of us and we cannot get reimbursed by the bus insurance then.

She had previously mentioned (2 days ago):

Hopefully we get a response soon as we only have 20 days before I’m forced to switch over to Turo insurance.

Main question: Does Turo only give hosts 30 days to resolve directly with the renters? Even if we are working together in good faith, and it takes some outside entity (e.g. NYC MTA) a long time to respond to a damage claim form then it will "default" to Turo insurance?

I know my insurance will "fight" for me since it is the bus driver's fault (confirmed by police report). Should I just submit to my insurance? Or tell the owner to chill out and give MTA more time to process the form? Thanks in advance