The "errors" in the arguments are not relevant. When surveying people who aren't disease biologists, it doesn't matter if there are specific one-way paths in the cutting edge research, what matters are the processes that inform the decisions. In the absence of any biological information, there's no indication to tilt the scales one way or another. If these people were saying 'well, robins have gene XYZZY which causes etc.', but they aren't, they're functioning on categories as they don't have any real information on cross-species disease. Accidental cancellation is not an example of a lack of bias.
If all gray squirrels hold this "disease" DNA, and are completely unaffected by it, it doesn't seem any more a disease than mitochondria or stomach flora. If there are gray squirrels without it, and they can contract it from red squirrels, then the disease does indeed pass both ways even though gray squirrels are asymptomatic.
Pointing out why an error in an element of the argument matters would be relevant.
1) the prototype model is correct,
He cites five papers that fairly well establish the prototype model within the domain of this discussion. If you don't like this sort of "presumption", and don't offer any sort of counter argument before calling it an "incredibly sloppy mistake", you've gone beyond the point of reasonable discussion.
2) that robins are closer to the prototype than ducks,
This is indeed the general finding, at least for Americans and presumably many other groups.
3) the reason people thought a disease transfer would be more likely from robins to ducks was because of this,
Can you give a good reason why the general public would think this? Can you support it non-anecdotally with high school biology that everyone remembers? Can you even defend more thoroughly the gray/red squirrel "disease" without hedging your definitions of disease?
4) the same pattern applies generally,
This was the finding when performed with numbers, states, and cities. Quick, describe the properties of the set {birds, numbers, states, cities}, and why the pattern doesn't apply outside of here.
The "errors" in the argument do little to diminish the fact that people, when given the option, favored robins over ducks. It's unlikely a "robin bias" exists.