Thats certainly true for giant hogweed. If everyone can cooperate its all very possible. Thats also interesting about JK. Fact its only spread by rhyzomes does make control possible.Coming from a river management background I'd suggest the key is the seed source. If you are getting fresh seed washed down a river onto your land each year (won't happen with JK as we only have the female here In the UK hence no viable seed - yet!) then you'll never eradicate it.
I sometimes think part of the problem is people overcomplicate it possibly to create a market for their expensive eradication service. This means nothing gets done.