If you looked side by side at an american mustang and a modern european warmblood or thoroughbred (after the introduction of arab and anglo-arab lines into european studbooks around the 17th century during an apparent period of fashionable anglomania in france), the missing link between them would be iberian horses like the lusitano and andalusian. It's not scientific, but mustangs are thought (colloquially) to be the descendents of escaped iberian horses both because of the plausibility of the shipwreck theory, and their general conformation. (shorter backed, roman noses, pointed ears, whereas up-hill withers are more of an artificial selective breeding trait) Another marker for iberian horses today is the common incidence of piraplasmosis, which may be interesting to see if it appears in those island horse bones, as it may indicate where the horse would have acquired it.

The andalusian and lusitano are often called baroque breeds and they have a more compact conformation and up-and-down movement that we refer to as "carriage-y" now because we think of pulling carriages, but the iberian horses were bred for their agility and bold temperament for cattle herding (bullfighting and skirmishing cavalry), so a shorter back (think turning a short wheelbase) gave them an advantage. Wild horses in the US weren't subject to the "lightening up" of the breed that introducing anglo-arabs into european studbooks did. But admittedly these are post-hoc explanations that pervade horse history.

The DNA evidence in the article confirms some ideas that I think had more rigor and reason than folklore, unless we treat historians and horsemen as folklorists.