You can negotiate, demand itemized bills, request a payment plan, etc., but there's no actual guarantee that those will be useful, and it can be a bit of effort. Sometimes your insurance also should cover something that they won't pay for, but getting the money from them is like pulling teeth.

TL;DR: You can fight the system, but no guarantees.

I called the insurance company about the bullshit "out of network ambulance" and they said they would "negotiate on our behalf", apparently. In the end we paid about $2200 for the ambulance if I remember right.

Everything else we paid sticker price. Fortunately I had some money in an HSA from a previous job so that helped.

(For people reading this who live in more civilized countries: an HSA is a special type of account where you can put money and not pay taxes on it, with the caveat that it can only be used for health expenses. It's similar to the much more common FSA, but with an FSA the account balance is reset to zero at the end of the year (not sure if the money goes to the government or the brokerage or what). This has led to a new absurd "FSA store" industry, where places sell only FSA-eligible items at a very high markup, with the idea being come December you'd rather buy their overpriced shit than just lose all the money outright. An HSA does not suffer from this nonsense (you keep the money indefinitely, because it's your money), but it seems like it's becoming more rare for an HSA to be offered on employer plans.)