Absolutely. The only reason it would be false is if:

- Google cared more about search quality than their ad business

- This kind of self-dealing were illegal, easily-prosecuted, and heavily fined

- Google were an ethical company

We know that all three of these are false, so we should assume Google is self-dealing. We've caught them (and every other large tech firm) doing it repeatedly.

I do know a great deal of sites that rank higher without ads compared to compeditors that do have ads ... but anecdotes are worthless and the only one who can answer are the people at google search.

Does https://ads.google.com/intl/en_us/home/campaigns/search-ads/ answer your question?

My question is about the websites that have installed google ads sense.

Let's say that my question does not cover the content that is directly sponsored with the search results.

No. Google does not intentionally publish details of their search ranking algorithm.

Is this in response to the recent leak?

I have heard this lots of times. I just wonder if it is true.

Did not know anything about a leak, to be honest.