Yes, throck, that opening sentence could be read the way you suggest but surely any confusion is removed by the fact that, printed underneath the grid in thick letters, is the word "Names:".
Actually, do they have more in common than being Spanish? The first names which emerged for me were Guardiola and Dali and I wasted a fair bit of time looking for another famous person from Catalunya before I figured out Cruz, who's from the Madrid area, was the third name.