but in a pragmatic sense, whatever difference separates a duck from a robin and would make a disease less likely to spread from a duck to a robin, must also be a difference between a robin and a duck, and would make a disease less likely to spread from a robin to a duck

What? No. It's not even vaguely reasonable to say that a transfer of a disease between two species is equally likely either way.

The differences between gray and red squirrels make it entirely certain that a particular disease will pass from gray to red, but not red to gray - grays carry the virus responsible in their DNA and are immune to it, but it kills reds.

Now, if you could show that people had a strong tendency to always assume that it would be easier to pass disease from something quite like the stereotypical example of a category to a non-stereotypical example than the other way around, you'd have something. As it is, you only have an anecdote.