We just had a discussion about this at a Native Plant Society walk this weekend with several people saying natives can be invasive, too. So yes they are a “thing” that people hear and talk about. I like to call them aggressive natives and prefer to leave the term invasive to alien plants but there is no denying that some natives are classified as noxious weeds, for example. Usually this happens in the context of them interfering negatively with agriculture, e.g. parasitic plants attacking crops or poisonous plants in pastures threatening the well-being of livestock grazing there. I find it ironic that often these cases of “invasive natives” involve a native species negatively impacting alien species introduced for human benefits (crops, livestock).