Right, the term might not inherently rest on that assumption, but the way that it is used does. If we were to consider anything that was a deliberate artifice of a creature artificial, then there'd be no problem, but common usage dictates that only humans are capable of creating artificial things. I suppose that the relevant case with your analogy would be if we were to call the phase change from liquid to solid in all other materials than water something other than freezing, then that usage would rather imply something special about water.
I also feel like you may be ignoring the complex interactions between humans and other organisms:
I don't think it is so clear cut as you suppose, nor that the way you use the term "artificial" is typical. For instance, many consider GM foods to be artificial, and organic foods to be natural. However, organic chicken is, by your definition, artificial- there is no such thing as a chicken without the artifice of humans. I agree, however, that the term can be useful, for instance, if we are talking about chemical substances that are found in nature, it is unhelpful for the semantic pedant to insist that all chemicals that exist are found in nature. I think my problem stems from people trying to force the concept onto the world and divide it neatly in two.
Quite.
A small quibble not really relevant to the debate- what is "artificiality"? Doesn't "artifice" express the same concept rather less clumsily?