Ah, a variation on that evergreen classic, "The Mexican Pet" - involving the couple vacationing in Mexico, who were said to have bought what they were told was a chihuahua but were later informed "by their vet" was a (wait for it) large rat. A staple in the urban legend repertoire since at least the '50s. The Daily Mail picture with this "story" showed an animal - who looked suspiciously photoshopped - that would not only have had to have been on the 'roids but also must have used a fur volumizer and a blow dryer to great effect.
Some stories are just that. Stories. They can be enjoyed but first they must be questioned for veracity. "The Argentinian Pet" is a variation of the tale above.