Many people leave Switzerland in summer believing that it is "covered" because they carry the card from the health box in their wallet. And it's true, within certain limits. The problem is that those limits matter, and sometimes they are discovered at the worst time.
The LAMal card has on the back the European Health Insurance Card (EHIC in its acronym in English, CEAM in French). This card gives access, in the EU countries, the EEA and the United Kingdom, to medically necessary benefits through the public system of the country where you are. Practically speaking: if you get sick in Spain and go to a Social Security doctor, the EHIC covers the same as it would for a Spanish citizen. The expenses you pay there do not count for or against your franchise or Swiss share. They are two independent systems.
The problem starts when someone goes to a private clinic thinking they are also covered, when they need a health repatriation, or when they travel outside the EU/EEA area. If you go to the United States, Japan or Mexico, LAMal only covers emergency treatments, and up to double what the same treatment would have cost in Switzerland. In countries where medical expenses are much higher than the Swiss, that can fall far short.
The practical summary: In Spain and the rest of the EU, the EHIC on the back of your health box card works well for urgent care in the public system. For private clinics, for repatriation, or for destinations outside Europe, supplementary travel insurance is required. It costs between 15 and 40 euros for a short trip. Many add-on boxes already include it. The reasonable thing to do is to check what you have before you leave, and not after the bill arrives.