Not really, they say:
The European Health Insurance Card (or EHIC) allows anyone who is insured by or covered by a statutory social security scheme of the EEA countries and Switzerland to receive medical treatment in another member state for free or at a reduced cost, if that treatment becomes necessary during their visit (for example, due to illness or an accident), or if they have a chronic pre-existing condition which requires care such as kidney dialysis.
The intention of the scheme is to allow people to continue their stay in a country without having to return home for medical care; as such, it does not cover people who have visited a country for the purpose of obtaining medical care, nor does it cover care, such as many types of dental treatment, which can be delayed until the visitor returns home.
It only covers healthcare which is normally covered by a statutory health care system in the visited country, so it does not render travel insurance obsolete.
Thanks the EHIC, you dont need to apply a state insurance in Switzerland also the international student & researcher health insurance plan provided through Swisscare is not necessary.
The card was phased in from 1 June 2004 and throughout 2005, becoming the sole healthcare entitlement document on 1 January 2006. The card is applicable in all French dependencies (DOM) as they are part of the EEA, but not all other self-governing territories such as Jersey or Aruba which are not.
It replaced the following medical forms:
E110 - For international road hauliers
E111 - For tourists
E119 - For unemployed/job seekers
E128 - For students and workers in another member state.