For a landlocked nation in the heart of Europe with no history of colonization or imperial foreign adventuring, the Swiss have rather a large soft spot for the Aboriginal peoples of the Americas.
First and foremost, Romanticism. The Swiss, as we know, have a wide and deep romantic streak that predisposes them to think in idealistic ways about indigenous life and its imagined independence, vigor, and spontaneous, unpretentious perfection.
Second, the idealized image of the North American (but, interestingly, almost never Central- or South American) 'Indian' is one which captures many values the Swiss hold dear. The perfect Indian lives in harmony with nature (most Swiss begrudgingly live in cities), and tidily divides his time between between the hard (but satisfying) graft of a life outdoors, and a quiver of altogether perfect Freizeit pursuits.
So it is that images of dubious indigeneity crop up everywhere, from Winnetou ice cream bars to this outstanding ad for Kytta:
The slogan, roughly translated as "An Indian Knows no Pain," would be remarkable if it were true, and would surely surprise North America's native peoples and their health care providers. Further, whether or not an 'Indian' feels pain surely has nothing to do with the efficacy of this antiphlogistine ointment; one who knows no pain ostensibly buys no pain relievers. Instead, it tells us a great deal about the people at whom the ad is directed, and for whom the 'Indian' is both the embodiment of a romantic ideal and a Baudrillardian simulacrum of the sort of life that many Swiss wish they were leading.
The Swiss love the Indian because he is quite possibly more Swiss than they are.