In general, if you misclassify "dog" for a fixed architecture you will most certainly misclassify "Blenheim Spaniel" and "Flat-coated Retriever" - the two other classes are subsets of the first. The "eats shoots and leaves" sentence is analogous to a "zoomed in" picture of fur - we don't know what it is but we are pretty sure what it isn't! This is still useful, and would already get most of the way there for large numbers of fur colors/patterns.
I think the concerns you have are more important at training time, but I have not seen a scenario where it has mattered very much. In general having good inference about these nets is really hard, but I think your initial thought about "dog space" ties in nicely to a post by Christopher Olah (http://christopherolah.wordpress.com/2014/04/09/neural-netwo...) - maybe you will find it interesting?
And yes it becomes really fascinating to extend your last thought to "optical illusions" and other tricks of the mind - even our own processing has paths are easily deceived and sometimes flat out wrong... so it is no surprise when something far inferior and less powerful also has trouble :)
Isn't it contextual - flat-coated retriever, well-done, but how good is it at picking one out of a pile of images of black animals, panthers, house cats?
It's a question of how visually coherent the category you're trying to learn is. From a purely visual perspective, the first two categories are relatively tightly bunched in the state space, whereas "dog" covers a diffuse cloud of appearances whose total range might even encompass the area where many non-dog animals also lie. Humans may rely on some additional semantic knowledge about different kinds of animal to produce an accurate classification. It's not entirely unlike how determining the meaning of the words in the phrase "eats shoots and leaves" can't be done reliably without incorporating contextual clues such as whether we were just talking about pandas or a murder in a restaurant.
There may also be issues around how distinct the categories are from each other. A couple years ago yours truly picked up a letter opener off the table and used it to spread butter on his toast, much to the amusement of his hosts.