Whether they have a monopoly or not is a question for the courts, I consider them to have a monopoly in search, apparently you do not. In the case that they don't have a monopoly in search then you're correct, but if they are found to have a monopoly then they could be found in violation.

Actually anti-trust law is about using the profits from one business to vertically integrate others by using the profits from one to subsidize the other. There is a modern component to it that revolves around consumer harm but anti-trust law was written as a means of redress for other businesses.

http://en.wikipedia.org/wiki/Standard_Oil#Monopoly_charges_a...