I have worked in health insurance and hospital financial management all my life and what Ms. Zaccarello wrote is nonsense.
What Italians call 'ticket' is nothing but a 'deductible' or 'co-pay' like we have in America, whether we have private commercial insurance or a public insurance like Medicare (which also has copays). Co-pays are imposed by insurers (and also by the Italian SSN, or Servizio Sanitario Nazionale) as a disincentive for overutilization. The copays Italians pay are on average much lower than what Americans pay in copayment, but either way the copay often is just a fraction of the overall cost of the service. For example, a commercial insurer in America typically imposes a co-payment of $150 for the ER. On average a ER bill going to an insurance company, after contractual allowances and discounts, is well over $500 and up just as a start for the simplest cases. I don't get to see a lot of ER bills lower than that. More typically they run into the thousands of $$. Obviously the $150 copay covers only a fraction of the cost, and is there only as a disincentive for subscribers to use the ER unless really necessary.
The Italian SSN introduced copays ('tickets') for ER in 2007. They vary from Region to region, and for some emergencies and some patients are not applied, but typically most regions have it at 25 euro. Italian costs are lower, but even in their case 25 euro represents only a fraction of what an ER service costs.
Regarding the relationship of Cost-Quality-Speed, that is true only in part. There are several dynamics that drive the US healthcare costs up, and are not all related to higher quality or higher speed. In part they are due to the disproportionately higher compensation of healthcare workers in America compared to Italy and other European countries, and healthcare is very labor intensive. The higher compensation is often driven by the shortage of these qualified workers, often determined by the excessive licensing requirements necessary to access those professions. Italy has some of the highest numbers of doctors and nurses per capita in the world, and their schools churn out a higher number of them yearly, therefore their salaries are lower simply as a result of demand and supply. Also, when I compare regulations with my relatives (some of whom are doctors and administrators in the Italian SSN) I note they don't have the stringent staff to patient ratios we are imposed in California, therefore they don't need to be as staffed with RNs as we are.
There are also issues related to excessive use of services ordered by physicians, sometimes unnecessarily. That is due to the different reimbursement schemes existing in the US compared to a National Universal system. The US system, based on a variety of commercial and public insurance payers, give incentive to doctors and hospital to order services in excess of what is needed and to over-invest in high end technology to attract customers. In America doctors or hospitals don't get paid unless they do something to you. In Italy the paymement schemes are based on capitation and hospitals have budgets determined by community needs and population health stats, so they don't have an incentive for you to show up at the doctor's office or at the hospital, on the contrary, they prefer if you stay home (and rather send the doctor to your house). The space here is not enough to explain this complicated matter, but the incentives-disincentives of the payment mechanisms are different, and our current US system incentivizes overutilization of services and over investment in technology, which forces providers to utilize more of it, even if not necessary, simply to recoup the depreciation costs. So the higher cost of the US system is not necessarily related to higher quality, and actually in many measures our outcomes are lower because our services are not as integrated as theirs.