Umm, I guess you could say that, but not really.
Most trainers in Black and White were given the elemental monkeys to be able to challenge your ingame trainer more, and the main purpose of the Elemental monkeys in general, was for the first gym to be harder, while also giving them to make it a lighter challenge.
Although they do appear to be the Starters of the First gym leaders,
For the rest I guess you could say they caught them in the forest.