“The driver of the minibus was not driving correctly,” Peter Lier, a 69-year-old former store manager from Bern, told a La Provincia newspaper reporter who visited him in hospital.
Lier, who broke a shoulder and several ribs in the accident, said the driver drove more than 100 metres down a sloping road with curves in third gear instead of second gear.
The Blick newspaper reported on Wednesday that a 66-year-old retired policeman from Wallisellen in the canton of Zurich died in the crash.
He was with his 71-year-old girlfriend from Zurich who was among those injured when the bus flipped over.
The couple were part of a group of 17 Swiss tourists, most of them retirees from German-speaking regions of Switzerland, who booked an “island hiking in the sun” tour with the Lucerne-based Baumeler Travel agency.
Lier told La Provincia he and other passengers grew alarmed at the way the bus was being driven and alerted the tour guide, a Swiss woman.
“But we did not want to say anything to the driver because he was so nice.”
The driver was among those injured.
Baumeler Reisen announced that 13 of the injured passengers have been returned to Switzerland, where they are being treated.
Three others, too badly hurt to be transported, are being cared for by Swiss medical practitioners sent to Gran Canaria.
Touring Club Schweiz and Rega both sent planes with aid teams to Gran Canaria, a popular holiday destination that forms part of the Canary Islands archipelago, lying 150 kilometres off the northwest coast of Africa.
Spanish police continue to investigate the accident.