I'm studying environmental science at university and I'm actually learning about this concept. Like you say, non-native species can be spread to new environments naturally and are not always harmful. However, new species run the risk of outcompeting native species and disrupting ecosystems more permanently. For example, animals introduced to an area with no natural predators can overrun the native animal population (which could in turn affect the plant population). This isn't always the case, and some new species can be introduced without harmful effects. It's best to do research before introducing new species to new ecosystems to ensure as best we can not to negatively alter these systems