It might take a while before the process is properly tuned and my guess is that outside of Europe, most of the exotics to native argument is effective.
Another example that made me wonder the same as you did with the Mute Swan, is how every Rock Pigeon in the UK and most parts of Europe are considered natives even though most plazas in these countries clearly have feral populations that have no breeding links with the cliff nesters of the region.
Or how Common Myna is clearly an exotic depending on which side of the Persian Gulf it's being reported, if it's Iran, they are all wild birds but if you see on in Kuwait, Qatar or UAE, then you clearly have an exotic absolutely no chance of it being a wind-blown bird; yet the reports of this species in Cyprus and Italy at clearly wild birds.
Overall, this is a great step in the right direction for many birders that like to count exotics but are not sure of their status (like the dozen or so species of parakeets in South Florida), but overall it needs some fine tuning if the data will be used for conservation studies and population trend data in the future, especially for the messy to tell apart exotics.
no breeding links with the cliff nesters of the region.
Not true. They interbreed where they come into contact... ...And how would anyone know?
Even if you were able to DNA test the birds using sufficiently discriminatory probes (SNPs or somesuch) I doubt that you'd find systematic differences. These are the same species...
great step in the right direction ...but are not sure of their status
I know enough to know that all the parakeets in Florida are introduced: don't need ebird to tell me that...
Where we have a species with a mix of natural and introduced individuals or populations (like mute swan, red kite, many ferruginous ducks in UK etc), then no-one, certainly not ebird, will be able to help. National rarity committees pronounce and decide whether a bird is "kosher", but I would only accept their decisions if I agreed with their reasoning. They cannot "know". Ultimately, if the animal is indistinguishable from the native form it doesn't matter to the ecology. Where it is distinguishable (parakeets) it's usually obviously an introduction. At what point an "introduction" becomes "native" ? (Before or after the last ice age? Is 17th century long enough ago for canada geese to be considered "native"? Is mode of introduction important—cattle egrets in UK =OK (but ultimately due to agricultural practices by man elsewhere), but canada geese =not?) This is clearly a moot, subjective point. Faunas are constantly evolving...
From the point of view of monitoring and science, all individual birds are equally valid. Because of the obsession with "natural purity", labelling species as exotic or introduced means birders are less likely to monitor them properly. We can see this false distinction because house sparrow is apparently native to the UK—but it's only here because we are (i.e. in some sense not different to canada geese).