Like almost all categories in nature, there are exceptions and ambiguities.
How do we really know a species is non-native? It might seem like an obvious category, but if you think about it, the "evidence" of absence before a certain date is just absence of evidence! I know taxonomists who don't agree that certain species, widely regarded as non-native, are actually non-native. They just think the species was under-collected before a certain date. This is especially true when there is no strong ecological or geophysical reason for the species not to have spread naturally. For example, species that are "native" to Eastern North America, but are considered "Introduced" in Western North America (e.g. American Bullfrog).
What about species that have both native and introduced genotypes? Phragmites australis is a classic example from North America, where you have to ID to subspecies (often very difficult) to distinguish the native from invasive. In iNat, if you only ID to species, it will say it is native. Only the observations that have been ID'd to species have the Introduced tag.
Other categories include:
Archaeophytes: plants which were probably introduced by humans to an area, but the introduction happened a very long time ago, and evidence is usually indirect. Most introductions before AD 1492 would fit in this category.
Neo-natives: This is a rather new term denoting species that settle without human assistance in a new region (see Essl et al. 2019). For example, range expansions due to global warming.
More discussion: https://forum.inaturalist.org/t/residency-status-for-archaeophyte-and-neo-native-plants/37252