Can non-native speakers of English become good TEFL teachers?

Can non-native speakers of English become good TEFL teachers?
This is a source of constant debate in the TEFL world. Here in Spain, many Spaniards (employers and students) request native speaker teachers. They hold beliefs, or prejudices, such as: British speak proper English not like Americans My German / Dutch /Spanish teacher of English knows grammar but speaks with a terrible accent I want ...