As this comment points out, there is a decent argument that searchers on Google or other engines aren't the ones creating the associations, and therefore perhaps Bing has no right to use that data.
The relationship between a term and a page was not created by Google, it was created by users. Google just indexes everything and makes note of these associations, but its does not create the link in the first place.
Going down this road of debate, we'll be getting into the semantics of "inventing" vs. "discovering."
Turning data into ranking is the whole purpose of a search engine, just as turning data into theory is the purpose of science, and turning experience into art is the purpose of art. Essentially here, we're debating whether search ranking is more like science, in which there's a correct answer that you are uncovering, or like art, in which all of the product is subjective.
Having worked in the field for five years, I'd argue that it is far closer to art than science. Google's rankings are its subjective determination, and the courts have agreed that Google's rankings are its constitutionally protected speech.
Though the data may all ultimately come from the human-created internet, the transformation of that data is still important, and subjective. To claim otherwise is to miss the whole point of search technology in the first place.