Replace AI with 'company' and you realize that we're living in that world already.
There's a reason it's called a Limited Liability Company. The whole point is to separate the company's liability from the individual that participates in it. For example, corporate financial liabilities of a company that is bankrupt.
You would not sue the nurse that makes a mistake. You would sue the company she works for. And if that company is bankrupt, well, that's it. There are rare instances where this isn't true, but generally it is.
Whether this is ethical or not, it's the system that we already have.
I don't think they meant the nurse would be responsible. The LLC would and should be fucked in that case.