That's one of the pluses of a large corporation's adaptations. The local variation won't be truly local. The variation used will be that considered the most quintessential by the entire country (in this case an Andalucian style of gazpacho made in Murcia by the Alvalle company).
There may be authentic Madrileņan gazpacho but I've never heard of it, so if I did pick out Gazpacho Madrileņo on a conventional restaurant's menu I'm just as likely to get fobbed off with an unauthentic concoction as any other visitor (my own expectation is that it would be a mixture of meat and unleavened bread in the Gazpacho Manchego style so this would be an easy expectation to anticipate and satisfy which would leave me none the wiser).