True to an extent, but in any city (100,000 or more people) there will be two hospitals and so the poor can choose which of the two to use. Note that by poor choosing only a small number need to have the practical ability (which is to say the almost middle class) to choose since a hospital will want to attract them and that ups service for everyone even thoose who couldn't reasonably get to the other hospital.
You know the hospitals in this scenario wouldn't be next door to each other, right? The extra 30 minutes of driving time it takes for me to get to my second-closest hospital could easily mean life or death.
For the person 15 minutes from either hospital there is a choice though. Trying to attract those middle people results in better services for those who are clearly closer to one hospital.
In addition to what other people have said about the impracticality of assuming choice, said hospitals will often not offer the same set of services, or will specialize in certain aspects of them.
You rarely have this choice in practice. Plus, as the article points out, even if you chose an in-network hospital you may well be seen by an out-of-network doctor.
In a free market the incentives are different though. in-network only is a thing because hospitals don't have any incentive to ensure everyone is in network.
