One thing that doesn't get mentioned a lot on this forum, is if you work en blanco, that is, work and pay taxes, the government provides you health insurance which you can use to go to the private hospitals.
Are you talking about obra social? Those aren't quite at the level of private health care and not all private hospitals will accept patients with obra social plans.
I provide OSDE for my employees. Yes, a portion of that is covered by the mandatory payment that I would have to pay on their behalf towards healthcare but as an employer, I pay the difference btwn what an obra social would cost and what OSDE costs for my employees. In the case of the young employees, the difference is negligible but in the case of some employees that are over the age of 36, I pay more than 1000 pesos a month for them to have OSDE.