It's mostly a deduction. The hypothesis is that if you can control what information is available you can affect the opinions and feelings of the people who receive that information.
Google is the dominant search engine and these days they even host the content through AMP and they own the most popular web browser and mobile computers operating system. They have not only the means to reach people and curate the content generated by other people, they can also change the content created by other people(AMP pages) and disguise their actions(since they control the app that displays the content).
Let's travel in time and go back to the WW2 days and mention Hitler as any proper online political discussion would eventually do.
Don't you think that it would be very convenient for Hitler if he had a way to show "how awful Jews are"? Wouldn't he loved it if Germans search results about economical crisis or gas prices would display how "greedy Jewish bankers are destroying the lives of honest German workers" or any other political or cultural Nazi propaganda?
Unless we switch to cryptographically signing all the content we create and learn to distrust any content that's not signed and have a way to verify that the signed content curation is not politically influenced, giants like Google and Facebook would have the power to make/break countries, start/stop lynches or even genocide.
There's a reason why China doesn't allow search results about Tiananmen Square protests of 1989 and all the governments are trying to find a way to control the information flow.
I see that claim thrown around a lot but nothing ever backs that up.