Hola Brad

The verb is in singular because it's agreeing with the percentage "un 62% de..." not the plural in "los lationoamericanos". This happens often with the partitives, for example:

Un tercio de los niños fue a la excursión.

A third of the kids went on the trip.

La mayoría de los estudiantes aprobó el examen.

The majority of the students passed the exam.

However, the agreement in plural would also be correct. You could also say:

"Un 62% de los latinoamericanos siguen una dieta especial."

Saludos

Inma