Remember, every person working for an insurer has unparalleled access to data on what the effects of their decision is going to be. You can't claim ignorance once you've seen the glorified spreadsheets that run these companies.
If you benefit from receiving stolen property, does the law force you to return it? One way of interpreting your scare quotes is that the executives turned a health insurer into a law violating company.
Obviously there are burdens of proof and this is most likely not possible to prosecute (it sounds like the health insurer has already shrunk and based on the date of the anecdote above, I’m guessing the relevant statutes of limitations have expired.
The general answer to that is: it depends on a lot of factors, but sometimes yes and sometimes no. The specific answer varies between jurisdictions, I think even between different US states and certainly between countries. It's often relevant whether you knew or should reasonably have known at the time of purchase that the property was stolen.
To be clear, I'm not expressing any kind of personal opinion here - I'm saying how the world actually works. Sometimes that matches what you are advocating, but sometimes not.
Of course, in both the mindset you advocate and in the other mindset, you have a claim against the person who stole your car, for sure, as well as anyone else who knowingly trafficked in the stolen goods.
Sometimes the relevant rules are different for real property vs personal property, and sometimes it matters whether the property's ownership has been registered in some register which the purchaser can verify before purchase. I don't think US car title records are generally publicly verifiable.
It's also usually relevant how the property was stolen - theft in the sense of actual larceny often has harsher consequences for the eventual bona fide purchaser (and more protections for the original owner) than if the property was stolen by fraudulently inducing the original owner to sign a deed of sale.
I'm avoiding giving specifics here because, again, the details vary by jurisdiction and by the particular facts and circumstances.