Depends on what's being investigated here, if the government would actually want to compel Google to alter their search results then it's a first amendment case.
The argument here is its unfair to bias ranking towards a preferred format. In this case, something about excluding competitors, except AMP is completely open-source[1] so...?
The counterargument is yes you can, because it's your pamphlet/newspaper/website and you're the editor, not the government.
Of course as a consumer, I don't really care whether it's some random company or Google who gets to violate my privacy, and I especially couldn't care less about lack of innovation in the privacy violation business, so I think the antitrust angle here is pretty slim.
[1] https://developers.google.com/analytics/devguides/collection...