No, not conned. The EHIC only covers basic medical healthcare - this is from the EHIC website.
"The EHIC is not an alternative to travel insurance. It will not cover any private medical healthcare or costs such as mountain rescue in ski resorts, being flown back to the UK, or lost or stolen property. Therefore, it is important to have both an EHIC and a valid private travel insurance policy. Some insurers now insist you hold an EHIC and many will waive the excess if you have one. For more information read our advice on travel insurance."